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Cell["Product Profitability Optimization", "Subsubtitle",
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 "Businesses typically have the capability to offer a variety of products. \
Given various factors such as the price at which the product may be sold, \
number of units that may be produced, resources required to produce each \
product, fixed and per unit overhead, etc., we would like to know which \
combination of products may produce the greatest profit for the company. This \
demonstration employs linear programming concepts to maximize profit for \
three products. The available resources for production are up to five \
employees. You may adjust the number of hours each resource is required for \
production per unit of each product type, as well as the hourly wage of the \
worker and the number of hours that worker is available per year. You may \
also specify the number of units you can produce each year, the selling price \
of the product, per unit and fixed annual overhead. As you adjust the \
parameters the two bar graphs will reflect the profit and number of each \
products to produce each year. \n\n",
 StyleBox["Adjustable Parameters", "Subsection"],
 "\n\n",
 StyleBox["Product",
  FontWeight->"Bold"],
 StyleBox["n",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox[" Price",
  FontWeight->"Bold"],
 " - unit price of Product #",
 StyleBox["n\n",
  FontSlant->"Italic"],
 StyleBox["Employee",
  FontWeight->"Bold"],
 StyleBox["m",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox[" Hourly Wage",
  FontWeight->"Bold"],
 " - amount paid Employee #m per hour\n",
 StyleBox["Product",
  FontWeight->"Bold"],
 StyleBox["n",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox[" Employee",
  FontWeight->"Bold"],
 StyleBox["m",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox[" Hours",
  FontWeight->"Bold"],
 " - number of hours required of Employee #",
 StyleBox["m",
  FontSlant->"Italic"],
 " for production of Product #",
 StyleBox["n",
  FontSlant->"Italic"],
 "\n",
 StyleBox["Annual Overhead",
  FontWeight->"Bold"],
 " - Fixed annual overhead exclusive of Product 1-5 overhead and wages (e.g. \
office rent, etc.)\n",
 StyleBox["Product",
  FontWeight->"Bold"],
 StyleBox["n ",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox["Overhead",
  FontWeight->"Bold"],
 " - variable overhead for Product #",
 StyleBox["n ",
  FontSlant->"Italic"],
 "exclusive of Employee 1-5 wages (e.g. materials cost)\n",
 StyleBox["Employee",
  FontWeight->"Bold"],
 StyleBox["n",
  FontWeight->"Bold",
  FontSlant->"Italic"],
 StyleBox[" Max Hours/Yr",
  FontWeight->"Bold"],
 " - Maximum hours Employee #",
 StyleBox["n",
  FontSlant->"Italic"],
 " is available per year (52 weeks * 40 hours = 2080)\n\n",
 StyleBox["Output Graphs", "Subsection"],
 "\n\nYou may click the + symbol to the right of the slider to see the actual \
value. As a change is made the bar graphs displayed to the right will change, \
showing the potential profit and the numbers of each product that would need \
to be sold to generate that profit. You may not edit the value field directly \
but you may make a large change in the slider value by clicking to the left \
or right of the slider indicator bar.\n\n",
 StyleBox["Profit",
  FontWeight->"Bold"],
 " - Shows the total profit from sales of Products 1-3 with the given \
constraints\n",
 StyleBox["Product Sales",
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 " - Shows the optimized number of Products 1-3 to sell\n\n",
 StyleBox["An Example", "Subsection"],
 "\n\nMemories Photography Studio photographs weddings and needs to determine \
which packages they should sell. They produce three types of wedding \
packages. Platinum is $5000, Gold is $1500, and Silver is $500. Memories has \
5 employees. Bob, the owner, is a Master Photographer and is in high demand. \
His assistant Carol is a talented photographer but not yet in quite as high \
demand as Bob. Marcia is the photo editor and creates the photo montages and \
wedding albums. Monica is Memories' Customer Care Executive and keeps things \
running smoothly for each wedding that Memories photographs. Diane is the \
office manager and handles sales and other business functions.\n\nMost \
weddings occur on weekends. Due to the work involved in producing the \
Platinum package, Memories can produce at most 50 Platinum packages per year. \
A Platinum package requires 12 hours of Bob's time, 12 hours of Carol's time, \
12 hours of Marcia's time, 16 hours of Monica's time, and 4 hours of Diane's \
time.  A Gold package requires 2 hours of Bob's time, 8 hours of Carol's \
time, 6 hours of Marcia's time, 4 hours of Monica's time, and 3 hours of \
Diane's time. Memories can produce up to 100 Gold packages per year. Since \
Bob is in such high demand he is only booked for Platinum and Gold weddings, \
so Carol photographs all of the Silver weddings. Memories can photograph up \
to 100 Silver weddings per year. A Silver package requires 4 hours of Carol's \
time, 2 hours of Marcia's time, 2 hours of Monica's time, and 2 hours of \
Diane's time. \n\nThe number of any one type of package that Memories can \
produce per year depends on the time required of the employees and the number \
of hours each employee is available each year. Bob is available 1000 hours \
per year, Carol 800 hours per year, Monica 2000 hours per year, Marcia 2000 \
hours per year, and Diane 2000 hours per year.\n\nEach employee gets an \
hourly wage based on the amount of work they spend on each wedding. Bob \
receives $80 per hour, Carol $45 per hour, Marcia $35 per hour, Monica $20 \
per hour, and Diane $25 her hour. \n\nMemories has fixed overhead costs for \
office rent, advertising, phones, etc. of $20,000 per year. Each package has \
a production cost. For Platinum it is $200, for Gold it is $100, and Siver it \
is $50 for each package sold.\n\nBob has a good handle on the costs, labor, \
and scheduling requirements for his different packages, but he's not sure how \
many of each he should sell. His marketing and growth strategy depends on \
providing the most profitable prodcut mix. Bob decided to ask for help.\n\n",
 StyleBox["Solution", "Subsubsection"],
 "\n\nThe Platinum, Gold, and Silver packages correspond to Products 1,2, and \
3. Set the price of each product accordingly (5000, 1500, 500). Next, set the \
hourly wages of Employees 1-5 (Bob = 80, Carol = 45, Marcia = 35, Monica = \
20, Diane = 25). Then set the time spent by each employee on each product \
(Product 1 Employee 1 corresponds to the 12 hours Bob spends on the Platinum \
package, etc.)  Set the fixed Annual Overhead (28000) and per package Product \
Overhead  for each product (250, 100, 50). Set the number of each package \
that Memories is capable of producing each year (50, 100, 100) and the number \
of hours each employee is available each year (1000,800,2000,2000,2000). The \
bar graphs show the profit potential and number of each package that would \
need to be sold to generate that profit. You may explore various scenarios by \
adjusting the available hours, hours spent on each package, selling price, \
etc. to determine what effect those parameters have on the optimization. \n\n\
This demonstration does not address potential scheduling conflicts between \
the packages that are sold other than taking into account the hours required \
by each employee and the maximum number of hours each employee can work each \
year. Further work could address scheduling and other pertinent issues.\n"
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Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`e1hoursx$$ = 1000, $CellContext`e2hoursx$$ =
     1000, $CellContext`e3hoursx$$ = 1000, $CellContext`e4hoursx$$ = 
    2000, $CellContext`e5hoursx$$ = 2000, $CellContext`overheadx$$ = 
    20000, $CellContext`p1capacityx$$ = 50, $CellContext`p1e1x$$ = 
    12, $CellContext`p1e2x$$ = 12, $CellContext`p1e3x$$ = 
    12, $CellContext`p1e4x$$ = 16, $CellContext`p1e5x$$ = 
    4, $CellContext`p1overheadx$$ = 200, $CellContext`p2capacityx$$ = 
    100, $CellContext`p2e1x$$ = 2, $CellContext`p2e2x$$ = 
    8, $CellContext`p2e3x$$ = 6, $CellContext`p2e4x$$ = 
    8, $CellContext`p2e5x$$ = 3, $CellContext`p2overheadx$$ = 
    100, $CellContext`p3capacityx$$ = 100, $CellContext`p3e1x$$ = 
    0, $CellContext`p3e2x$$ = 4, $CellContext`p3e3x$$ = 
    2, $CellContext`p3e4x$$ = 2, $CellContext`p3e5x$$ = 
    2, $CellContext`p3overheadx$$ = 50, $CellContext`price1x$$ = 
    5000, $CellContext`price2x$$ = 1500, $CellContext`price3x$$ = 
    500, $CellContext`s1x$$ = 80, $CellContext`s2x$$ = 
    45, $CellContext`s3x$$ = 35, $CellContext`s4x$$ = 20, $CellContext`s5x$$ =
     25, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`price1x$$], 5000, "Product1 Price"}, 0, 5000, 
      100}, {{
       Hold[$CellContext`price2x$$], 1500, "Product2 Price"}, 0, 5000, 
      100}, {{
       Hold[$CellContext`price3x$$], 500, "Product3 Price"}, 0, 5000, 100}, {{
      
       Hold[$CellContext`s1x$$], 80, "Employee1 Hourly Wage"}, 5, 200, 1}, {{
       Hold[$CellContext`s2x$$], 45, "Employee2 Hourly Wage"}, 5, 200, 1}, {{
       Hold[$CellContext`s3x$$], 35, "Employee3 Hourly Wage"}, 5, 200, 1}, {{
       Hold[$CellContext`s4x$$], 20, "Employee4 Hourly Wage"}, 5, 200, 1}, {{
       Hold[$CellContext`s5x$$], 25, "Employee5 Hourly Wage"}, 5, 200, 1}, {{
       Hold[$CellContext`p1e1x$$], 12, "Product1 Employee1 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p2e1x$$], 2, "Product2 Employee1 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p3e1x$$], 0, "Product3 Employee1 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p1e2x$$], 12, "Product1 Employee2 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p2e2x$$], 8, "Product2 Employee2 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p3e2x$$], 4, "Product3 Employee2 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p1e3x$$], 12, "Product1 Employee3 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p2e3x$$], 6, "Product2 Employee3 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p3e3x$$], 2, "Product3 Employee3 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p1e4x$$], 16, "Product1 Employee4 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p2e4x$$], 8, "Product2 Employee4 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p3e4x$$], 2, "Product3 Employee4 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p1e5x$$], 4, "Product1 Employee5 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p2e5x$$], 3, "Product2 Employee5 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`p3e5x$$], 2, "Product3 Employee5 Hours"}, 0, 20, 
      1}, {{
       Hold[$CellContext`overheadx$$], 20000, "Annual Overhead"}, 0, 100000, 
      1000}, {{
       Hold[$CellContext`e1hoursx$$], 1000, "Employee1 Max Hours/Yr"}, 100, 
      2000, 100}, {{
       Hold[$CellContext`e2hoursx$$], 1000, "Employee2 Max Hours/Yr"}, 100, 
      2000, 100}, {{
       Hold[$CellContext`e3hoursx$$], 1000, "Employee3 Max Hours/Yr"}, 100, 
      2000, 100}, {{
       Hold[$CellContext`e4hoursx$$], 2000, "Employee4 Max Hours/Yr"}, 100, 
      2000, 100}, {{
       Hold[$CellContext`e5hoursx$$], 2000, "Employee5 Max Hours/Yr"}, 100, 
      2000, 100}, {{
       Hold[$CellContext`p1capacityx$$], 50, "Product1 Annual Capacity"}, 10, 
      200, 10}, {{
       Hold[$CellContext`p2capacityx$$], 100, "Product2 Annual Capacity"}, 10,
       200, 10}, {{
       Hold[$CellContext`p3capacityx$$], 100, "Product3 Annual Capacity"}, 10,
       200, 10}, {{
       Hold[$CellContext`p1overheadx$$], 200, "Product1 Overhead"}, 0, 1000, 
      10}, {{
       Hold[$CellContext`p2overheadx$$], 100, "Product2 Overhead"}, 0, 1000, 
      10}, {{
       Hold[$CellContext`p3overheadx$$], 50, "Product3 Overhead"}, 0, 1000, 
      10}}, Typeset`size$$ = {278., {270., 278.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    False, $CellContext`price1x$5615$$ = 0, $CellContext`price2x$5616$$ = 
    0, $CellContext`price3x$5617$$ = 0, $CellContext`s1x$5618$$ = 
    0, $CellContext`s2x$5619$$ = 0, $CellContext`s3x$5620$$ = 
    0, $CellContext`s4x$5621$$ = 0, $CellContext`s5x$5622$$ = 
    0, $CellContext`p1e1x$5623$$ = 0, $CellContext`p2e1x$5624$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`e1hoursx$$ = 1000, $CellContext`e2hoursx$$ = 
        1000, $CellContext`e3hoursx$$ = 1000, $CellContext`e4hoursx$$ = 
        2000, $CellContext`e5hoursx$$ = 2000, $CellContext`overheadx$$ = 
        20000, $CellContext`p1capacityx$$ = 50, $CellContext`p1e1x$$ = 
        12, $CellContext`p1e2x$$ = 12, $CellContext`p1e3x$$ = 
        12, $CellContext`p1e4x$$ = 16, $CellContext`p1e5x$$ = 
        4, $CellContext`p1overheadx$$ = 200, $CellContext`p2capacityx$$ = 
        100, $CellContext`p2e1x$$ = 2, $CellContext`p2e2x$$ = 
        8, $CellContext`p2e3x$$ = 6, $CellContext`p2e4x$$ = 
        8, $CellContext`p2e5x$$ = 3, $CellContext`p2overheadx$$ = 
        100, $CellContext`p3capacityx$$ = 100, $CellContext`p3e1x$$ = 
        0, $CellContext`p3e2x$$ = 4, $CellContext`p3e3x$$ = 
        2, $CellContext`p3e4x$$ = 2, $CellContext`p3e5x$$ = 
        2, $CellContext`p3overheadx$$ = 50, $CellContext`price1x$$ = 
        5000, $CellContext`price2x$$ = 1500, $CellContext`price3x$$ = 
        500, $CellContext`s1x$$ = 80, $CellContext`s2x$$ = 
        45, $CellContext`s3x$$ = 35, $CellContext`s4x$$ = 
        20, $CellContext`s5x$$ = 25}, "ControllerVariables" :> {
        Hold[$CellContext`price1x$$, $CellContext`price1x$5615$$, 0], 
        Hold[$CellContext`price2x$$, $CellContext`price2x$5616$$, 0], 
        Hold[$CellContext`price3x$$, $CellContext`price3x$5617$$, 0], 
        Hold[$CellContext`s1x$$, $CellContext`s1x$5618$$, 0], 
        Hold[$CellContext`s2x$$, $CellContext`s2x$5619$$, 0], 
        Hold[$CellContext`s3x$$, $CellContext`s3x$5620$$, 0], 
        Hold[$CellContext`s4x$$, $CellContext`s4x$5621$$, 0], 
        Hold[$CellContext`s5x$$, $CellContext`s5x$5622$$, 0], 
        Hold[$CellContext`p1e1x$$, $CellContext`p1e1x$5623$$, 0], 
        Hold[$CellContext`p2e1x$$, $CellContext`p2e1x$5624$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`f0 = $CellContext`f[$CellContext`price1x$$, \
$CellContext`price2x$$, $CellContext`price3x$$, $CellContext`s1x$$, \
$CellContext`s2x$$, $CellContext`s3x$$, $CellContext`s4x$$, \
$CellContext`s5x$$, $CellContext`p1e1x$$, $CellContext`p1e2x$$, \
$CellContext`p1e3x$$, $CellContext`p1e4x$$, $CellContext`p1e5x$$, \
$CellContext`p2e1x$$, $CellContext`p2e2x$$, $CellContext`p2e3x$$, \
$CellContext`p2e4x$$, $CellContext`p2e5x$$, $CellContext`p3e1x$$, \
$CellContext`p3e2x$$, $CellContext`p3e3x$$, $CellContext`p3e4x$$, \
$CellContext`p3e5x$$, $CellContext`overheadx$$, $CellContext`e1hoursx$$, \
$CellContext`e2hoursx$$, $CellContext`e3hoursx$$, $CellContext`e4hoursx$$, \
$CellContext`e5hoursx$$, $CellContext`p1capacityx$$, \
$CellContext`p2capacityx$$, $CellContext`p3capacityx$$, \
$CellContext`p1overheadx$$, $CellContext`p1overheadx$$, \
$CellContext`p1overheadx$$]; GraphicsColumn[{
          BarCharts`BarChart[{
            Part[$CellContext`f0, 1]}, BarCharts`BarStyle -> 
           Directive[Green, 
             Opacity[0.5]], BarCharts`BarLabels -> {}, Frame -> True, 
           FrameLabel -> {"All Products", "Profit"}, ImageSize -> {200, 200}],
           
          BarCharts`BarChart[{
            ReplaceAll[{$CellContext`p1, $CellContext`p2, $CellContext`p3}, 
             Part[$CellContext`f0, 2]]}, BarCharts`BarStyle -> 
           Directive[Yellow, 
             Opacity[0.5]], 
           BarCharts`BarLabels -> {"Product 1", "Product 2", "Product 3"}, 
           Frame -> True, FrameLabel -> {"Product Sales", "Qty"}, 
           ImageSize -> {200, 200}]}]), 
      "Specifications" :> {{{$CellContext`price1x$$, 5000, "Product1 Price"}, 
         0, 5000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`price2x$$, 1500, "Product2 Price"}, 0, 
         5000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`price3x$$, 500, "Product3 Price"}, 0, 
         5000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`s1x$$, 80, "Employee1 Hourly Wage"}, 5, 
         200, 1, Appearance -> 
         "Labeled"}, {{$CellContext`s2x$$, 45, "Employee2 Hourly Wage"}, 5, 
         200, 1, Appearance -> 
         "Labeled"}, {{$CellContext`s3x$$, 35, "Employee3 Hourly Wage"}, 5, 
         200, 1, Appearance -> 
         "Labeled"}, {{$CellContext`s4x$$, 20, "Employee4 Hourly Wage"}, 5, 
         200, 1, Appearance -> 
         "Labeled"}, {{$CellContext`s5x$$, 25, "Employee5 Hourly Wage"}, 5, 
         200, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p1e1x$$, 12, "Product1 Employee1 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p2e1x$$, 2, "Product2 Employee1 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p3e1x$$, 0, "Product3 Employee1 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p1e2x$$, 12, "Product1 Employee2 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p2e2x$$, 8, "Product2 Employee2 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p3e2x$$, 4, "Product3 Employee2 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p1e3x$$, 12, "Product1 Employee3 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p2e3x$$, 6, "Product2 Employee3 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p3e3x$$, 2, "Product3 Employee3 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p1e4x$$, 16, "Product1 Employee4 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p2e4x$$, 8, "Product2 Employee4 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p3e4x$$, 2, "Product3 Employee4 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p1e5x$$, 4, "Product1 Employee5 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p2e5x$$, 3, "Product2 Employee5 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`p3e5x$$, 2, "Product3 Employee5 Hours"}, 
         0, 20, 1, Appearance -> 
         "Labeled"}, {{$CellContext`overheadx$$, 20000, "Annual Overhead"}, 0,
          100000, 1000, Appearance -> 
         "Labeled"}, {{$CellContext`e1hoursx$$, 1000, 
          "Employee1 Max Hours/Yr"}, 100, 2000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`e2hoursx$$, 1000, 
          "Employee2 Max Hours/Yr"}, 100, 2000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`e3hoursx$$, 1000, 
          "Employee3 Max Hours/Yr"}, 100, 2000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`e4hoursx$$, 2000, 
          "Employee4 Max Hours/Yr"}, 100, 2000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`e5hoursx$$, 2000, 
          "Employee5 Max Hours/Yr"}, 100, 2000, 100, Appearance -> 
         "Labeled"}, {{$CellContext`p1capacityx$$, 50, 
          "Product1 Annual Capacity"}, 10, 200, 10, Appearance -> 
         "Labeled"}, {{$CellContext`p2capacityx$$, 100, 
          "Product2 Annual Capacity"}, 10, 200, 10, Appearance -> 
         "Labeled"}, {{$CellContext`p3capacityx$$, 100, 
          "Product3 Annual Capacity"}, 10, 200, 10, Appearance -> 
         "Labeled"}, {{$CellContext`p1overheadx$$, 200, "Product1 Overhead"}, 
         0, 1000, 10, Appearance -> 
         "Labeled"}, {{$CellContext`p2overheadx$$, 100, "Product2 Overhead"}, 
         0, 1000, 10, Appearance -> 
         "Labeled"}, {{$CellContext`p3overheadx$$, 50, "Product3 Overhead"}, 
         0, 1000, 10, Appearance -> "Labeled"}}, "Options" :> {}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{803., {591.5, 598.5}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`f0 = {
        256500, {$CellContext`p1 -> 50, $CellContext`p2 -> 
          100, $CellContext`p3 -> 100}}, $CellContext`f[
         Pattern[$CellContext`price1, 
          Blank[]], 
         Pattern[$CellContext`price2, 
          Blank[]], 
         Pattern[$CellContext`price3, 
          Blank[]], 
         Pattern[$CellContext`s1, 
          Blank[]], 
         Pattern[$CellContext`s2, 
          Blank[]], 
         Pattern[$CellContext`s3, 
          Blank[]], 
         Pattern[$CellContext`s4, 
          Blank[]], 
         Pattern[$CellContext`s5, 
          Blank[]], 
         Pattern[$CellContext`p1e1, 
          Blank[]], 
         Pattern[$CellContext`p1e2, 
          Blank[]], 
         Pattern[$CellContext`p1e3, 
          Blank[]], 
         Pattern[$CellContext`p1e4, 
          Blank[]], 
         Pattern[$CellContext`p1e5, 
          Blank[]], 
         Pattern[$CellContext`p2e1, 
          Blank[]], 
         Pattern[$CellContext`p2e2, 
          Blank[]], 
         Pattern[$CellContext`p2e3, 
          Blank[]], 
         Pattern[$CellContext`p2e4, 
          Blank[]], 
         Pattern[$CellContext`p2e5, 
          Blank[]], 
         Pattern[$CellContext`p3e1, 
          Blank[]], 
         Pattern[$CellContext`p3e2, 
          Blank[]], 
         Pattern[$CellContext`p3e3, 
          Blank[]], 
         Pattern[$CellContext`p3e4, 
          Blank[]], 
         Pattern[$CellContext`p3e5, 
          Blank[]], 
         Pattern[$CellContext`overhead, 
          Blank[]], 
         Pattern[$CellContext`e1hours, 
          Blank[]], 
         Pattern[$CellContext`e2hours, 
          Blank[]], 
         Pattern[$CellContext`e3hours, 
          Blank[]], 
         Pattern[$CellContext`e4hours, 
          Blank[]], 
         Pattern[$CellContext`e5hours, 
          Blank[]], 
         Pattern[$CellContext`p1capacity, 
          Blank[]], 
         Pattern[$CellContext`p2capacity, 
          Blank[]], 
         Pattern[$CellContext`p3capacity, 
          Blank[]]] := 
       Maximize[{$CellContext`p1 ($CellContext`price1 - ($CellContext`p1e1 \
$CellContext`s1 + $CellContext`p1e2 $CellContext`s2 + $CellContext`p1e3 \
$CellContext`s3 + $CellContext`p1e4 $CellContext`s4 + $CellContext`p1e5 \
$CellContext`s5)) + $CellContext`p2 ($CellContext`price2 - ($CellContext`p2e1 \
$CellContext`s1 + $CellContext`p2e2 $CellContext`s2 + $CellContext`p2e3 \
$CellContext`s3 + $CellContext`p2e4 $CellContext`s4 + $CellContext`p2e5 \
$CellContext`s5)) + $CellContext`p3 ($CellContext`price3 - ($CellContext`p3e1 \
$CellContext`s1 + $CellContext`p3e2 $CellContext`s2 + $CellContext`p3e3 \
$CellContext`s3 + $CellContext`p3e4 $CellContext`s4 + $CellContext`p3e5 \
$CellContext`s5)) - $CellContext`overhead, $CellContext`p1 $CellContext`p1e1 + \
$CellContext`p2 $CellContext`p2e1 + $CellContext`p3 $CellContext`p3e1 <= \
$CellContext`e1hours, $CellContext`p1 $CellContext`p1e2 + $CellContext`p2 \
$CellContext`p2e2 + $CellContext`p3 $CellContext`p2e3 <= \
$CellContext`e2hours, $CellContext`p1 $CellContext`p1e3 + $CellContext`p2 \
$CellContext`p2e3 + $CellContext`p3 $CellContext`p3e3 <= \
$CellContext`e3hours, $CellContext`p1 $CellContext`p1e4 + $CellContext`p2 \
$CellContext`p2e4 + $CellContext`p3 $CellContext`p3e4 <= \
$CellContext`e4hours, $CellContext`p1 $CellContext`p1e5 + $CellContext`p2 \
$CellContext`p2e5 + $CellContext`p3 $CellContext`p3e5 <= \
$CellContext`e5hours, $CellContext`p1 <= $CellContext`p1capacity, \
$CellContext`p2 <= $CellContext`p2capacity, $CellContext`p3 <= \
$CellContext`p3capacity, $CellContext`p1 >= 0, $CellContext`p2 >= 
          0, $CellContext`p3 >= 
          0}, {$CellContext`p1, $CellContext`p2, $CellContext`p3}], \
$CellContext`f[
         Pattern[$CellContext`price1, 
          Blank[]], 
         Pattern[$CellContext`price2, 
          Blank[]], 
         Pattern[$CellContext`price3, 
          Blank[]], 
         Pattern[$CellContext`s1, 
          Blank[]], 
         Pattern[$CellContext`s2, 
          Blank[]], 
         Pattern[$CellContext`s3, 
          Blank[]], 
         Pattern[$CellContext`s4, 
          Blank[]], 
         Pattern[$CellContext`s5, 
          Blank[]], 
         Pattern[$CellContext`p1e1, 
          Blank[]], 
         Pattern[$CellContext`p1e2, 
          Blank[]], 
         Pattern[$CellContext`p1e3, 
          Blank[]], 
         Pattern[$CellContext`p1e4, 
          Blank[]], 
         Pattern[$CellContext`p1e5, 
          Blank[]], 
         Pattern[$CellContext`p2e1, 
          Blank[]], 
         Pattern[$CellContext`p2e2, 
          Blank[]], 
         Pattern[$CellContext`p2e3, 
          Blank[]], 
         Pattern[$CellContext`p2e4, 
          Blank[]], 
         Pattern[$CellContext`p2e5, 
          Blank[]], 
         Pattern[$CellContext`p3e1, 
          Blank[]], 
         Pattern[$CellContext`p3e2, 
          Blank[]], 
         Pattern[$CellContext`p3e3, 
          Blank[]], 
         Pattern[$CellContext`p3e4, 
          Blank[]], 
         Pattern[$CellContext`p3e5, 
          Blank[]], 
         Pattern[$CellContext`overhead, 
          Blank[]], 
         Pattern[$CellContext`e1hours, 
          Blank[]], 
         Pattern[$CellContext`e2hours, 
          Blank[]], 
         Pattern[$CellContext`e3hours, 
          Blank[]], 
         Pattern[$CellContext`e4hours, 
          Blank[]], 
         Pattern[$CellContext`e5hours, 
          Blank[]], 
         Pattern[$CellContext`p1capacity, 
          Blank[]], 
         Pattern[$CellContext`p2capacity, 
          Blank[]], 
         Pattern[$CellContext`p3capacity, 
          Blank[]], 
         Pattern[$CellContext`p1overhead, 
          Blank[]], 
         Pattern[$CellContext`p2overhead, 
          Blank[]], 
         Pattern[$CellContext`p3overhead, 
          Blank[]]] := 
       Maximize[{$CellContext`p1 ($CellContext`price1 - ($CellContext`p1e1 \
$CellContext`s1 + $CellContext`p1e2 $CellContext`s2 + $CellContext`p1e3 \
$CellContext`s3 + $CellContext`p1e4 $CellContext`s4 + $CellContext`p1e5 \
$CellContext`s5 + $CellContext`p1overhead)) + $CellContext`p2 \
($CellContext`price2 - ($CellContext`p2e1 $CellContext`s1 + $CellContext`p2e2 \
$CellContext`s2 + $CellContext`p2e3 $CellContext`s3 + $CellContext`p2e4 \
$CellContext`s4 + $CellContext`p2e5 $CellContext`s5 + \
$CellContext`p2overhead)) + $CellContext`p3 ($CellContext`price3 - \
($CellContext`p3e1 $CellContext`s1 + $CellContext`p3e2 $CellContext`s2 + \
$CellContext`p3e3 $CellContext`s3 + $CellContext`p3e4 $CellContext`s4 + \
$CellContext`p3e5 $CellContext`s5 + $CellContext`p3overhead)) - \
$CellContext`overhead, $CellContext`p1 $CellContext`p1e1 + $CellContext`p2 \
$CellContext`p2e1 + $CellContext`p3 $CellContext`p3e1 <= \
$CellContext`e1hours, $CellContext`p1 $CellContext`p1e2 + $CellContext`p2 \
$CellContext`p2e2 + $CellContext`p3 $CellContext`p2e3 <= \
$CellContext`e2hours, $CellContext`p1 $CellContext`p1e3 + $CellContext`p2 \
$CellContext`p2e3 + $CellContext`p3 $CellContext`p3e3 <= \
$CellContext`e3hours, $CellContext`p1 $CellContext`p1e4 + $CellContext`p2 \
$CellContext`p2e4 + $CellContext`p3 $CellContext`p3e4 <= \
$CellContext`e4hours, $CellContext`p1 $CellContext`p1e5 + $CellContext`p2 \
$CellContext`p2e5 + $CellContext`p3 $CellContext`p3e5 <= \
$CellContext`e5hours, $CellContext`p1 <= $CellContext`p1capacity, \
$CellContext`p2 <= $CellContext`p2capacity, $CellContext`p3 <= \
$CellContext`p3capacity, $CellContext`p1 >= 0, $CellContext`p2 >= 
          0, $CellContext`p3 >= 0, Plus[$CellContext`p1overhead] >= 0, 
          Plus[$CellContext`p2overhead] >= 0, $CellContext`p3overhead >= 
          0}, {$CellContext`p1, $CellContext`p2, $CellContext`p3}], 
       BarCharts`BarChart[
         Pattern[BarCharts`Private`idata, 
          Repeated[{
            Repeated[
             PatternTest[
              Blank[], BarCharts`Private`numberQ]]}]], 
         Pattern[BarCharts`Private`opts, 
          OptionsPattern[]]] := 
       BarCharts`BarChart[{BarCharts`Private`idata}, BarCharts`Private`opts], 
       BarCharts`BarChart[
         PatternTest[
          Pattern[BarCharts`Private`idata, 
           Blank[]], VectorQ[#, VectorQ[#, BarCharts`Private`numberQ]& ]& ], 
         Pattern[BarCharts`Private`opts, 
          OptionsPattern[]]] := 
       Module[{BarCharts`Private`data = BarCharts`Private`idata, 
          BarCharts`Private`ln = Length[BarCharts`Private`idata], 
          BarCharts`Private`ticks, BarCharts`Private`orig, 
          BarCharts`Private`rng, BarCharts`Private`lns = 
          Map[Length, BarCharts`Private`idata], BarCharts`Private`bs, 
          BarCharts`Private`bgs, BarCharts`Private`labels, 
          BarCharts`Private`width, 
          BarCharts`Private`gbopts}, {
           BarCharts`Private`bs, BarCharts`Private`bgs, 
            BarCharts`Private`labels, BarCharts`Private`orient} = 
          ReplaceAll[{
            BarCharts`BarSpacing, BarCharts`BarGroupSpacing, 
             BarCharts`BarLabels, BarCharts`BarOrientation}, 
            Flatten[{BarCharts`Private`opts, 
              Options[BarCharts`BarChart]}]]; 
         BarCharts`Private`gbopts = FilterRules[
            Options[BarCharts`BarChart], 
            Options[BarCharts`GeneralizedBarChart]]; 
         BarCharts`Private`bs = N[BarCharts`Private`bs]; 
         BarCharts`Private`bgs = N[BarCharts`Private`bgs]; 
         If[BarCharts`Private`bs === Automatic, BarCharts`Private`bs = 0.03]; 
         If[BarCharts`Private`bgs === Automatic, BarCharts`Private`bgs = 0.2]; 
         Which[BarCharts`Private`labels === Automatic, 
           BarCharts`Private`labels = Range[
             Max[BarCharts`Private`lns]], BarCharts`Private`labels === None, 
           Null, BarCharts`Private`labels === {}, BarCharts`Private`labels = 
           None, True, BarCharts`Private`labels = 
           BarCharts`Private`CycleValues[BarCharts`Private`labels, 
             Max[BarCharts`Private`lns]]]; 
         BarCharts`Private`width = (1 - BarCharts`Private`bgs)/
           BarCharts`Private`ln; 
         BarCharts`Private`data = 
          MapIndexed[{
            Part[#2, 2] + BarCharts`Private`width (Part[#2, 1] - 1), #, 
             BarCharts`Private`width - BarCharts`Private`bs}& , 
            BarCharts`Private`idata, {2}]; 
         If[BarCharts`Private`labels =!= None, BarCharts`Private`ticks = {
             Transpose[{Range[
                 Max[BarCharts`Private`lns]] + ((BarCharts`Private`ln - 1) 
                 BarCharts`Private`width)/2, BarCharts`Private`labels, 
               Table[0, {
                 Max[BarCharts`Private`lns]}]}], Automatic}, 
           BarCharts`Private`ticks = {None, Automatic}; Null]; 
         BarCharts`Private`orig = {
           1 - BarCharts`Private`width/2 - BarCharts`Private`bgs, 0}; 
         BarCharts`Private`rng = {{
            1 - BarCharts`Private`width/2 - BarCharts`Private`bgs, 
             Max[BarCharts`Private`lns] + (BarCharts`Private`ln - 1/2) 
              BarCharts`Private`width + BarCharts`Private`bgs}, All}; 
         If[BarCharts`Private`orient === Horizontal, 
           BarCharts`Private`ticks = Reverse[BarCharts`Private`ticks]; 
           BarCharts`Private`orig = Reverse[BarCharts`Private`orig]; 
           BarCharts`Private`rng = Reverse[BarCharts`Private`rng]]; 
         BarCharts`GeneralizedBarChart[
          BarCharts`Private`data, BarCharts`Private`opts, Ticks -> 
           BarCharts`Private`ticks, AxesOrigin -> BarCharts`Private`orig, 
           PlotRange -> BarCharts`Private`rng, FrameTicks -> 
           BarCharts`Private`ticks, BarCharts`Private`gbopts]], 
       BarCharts`BarChart[
         Pattern[BarCharts`Private`list, {
           Repeated[{
             PatternTest[
              Blank[], BarCharts`Private`numberQ], 
             Blank[]}]}], 
         PatternTest[
          Pattern[BarCharts`Private`opts, 
           BlankNullSequence[]], OptionQ]] := 
       Module[{BarCharts`Private`lab, 
          BarCharts`Private`dat}, {
           BarCharts`Private`dat, BarCharts`Private`lab} = 
          Transpose[BarCharts`Private`list]; 
         BarCharts`BarChart[
          BarCharts`Private`dat, BarCharts`Private`opts, BarCharts`BarLabels -> 
           BarCharts`Private`lab]], BarCharts`BarChart[
         Pattern[BarCharts`Private`list, {
           Repeated[{
             PatternTest[
              Blank[], BarCharts`Private`numberQ], 
             Blank[], 
             Blank[]}]}], 
         PatternTest[
          Pattern[BarCharts`Private`opts, 
           BlankNullSequence[]], OptionQ]] := 
       Module[{BarCharts`Private`lab, BarCharts`Private`sty, 
          BarCharts`Private`dat}, {
           BarCharts`Private`dat, BarCharts`Private`lab, 
            BarCharts`Private`sty} = Transpose[BarCharts`Private`list]; 
         BarCharts`BarChart[
          BarCharts`Private`dat, BarCharts`Private`opts, BarCharts`BarLabels -> 
           BarCharts`Private`lab, BarCharts`BarStyle -> 
           BarCharts`Private`sty]], 
       Options[BarCharts`BarChart] := {
        AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> 
         True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, 
         Background -> None, BarCharts`BarEdges -> True, 
         BarCharts`BarEdgeStyle -> Opacity[0.5], BarCharts`BarGroupSpacing -> 
         Automatic, BarCharts`BarLabels -> Automatic, 
         BarCharts`BarOrientation -> Vertical, BarCharts`BarSpacing -> 
         Automatic, BarCharts`BarStyle -> Automatic, BarCharts`BarValues -> 
         False, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> 
         Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> 
         False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic,
          FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, 
         ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, 
         LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> 
         All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, 
         PlotRegion -> Automatic, PreserveImageOptions -> Automatic, 
         Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, 
         TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> 
         TraditionalForm}, 
       TagSet[BarCharts`BarChart, 
        MessageName[BarCharts`BarChart, "usage"], 
        "\!\(\*RowBox[{\"BarChart\", \"[\", RowBox[{\"{\", \
RowBox[{SubscriptBox[StyleBox[\"y\", \"TI\"], StyleBox[\"1\", \"TR\"]], \
\",\", SubscriptBox[StyleBox[\"y\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \
StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \"]\"}]\) generates a bar chart \
of the values \!\(\*RowBox[{SubscriptBox[StyleBox[\"y\", \"TI\"], \
StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"y\", \"TI\"], \
StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}]\).\n\!\(\
\*RowBox[{\"BarChart\", \"[\", RowBox[{\"{\", \
RowBox[{SubscriptBox[StyleBox[\"list\", \"TI\"], StyleBox[\"1\", \"TR\"]], \
\",\", SubscriptBox[StyleBox[\"list\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\
\", StyleBox[\"\[Ellipsis]\", \"TI\"]}], \"}\"}], \"]\"}]\) generates a bar \
chart of the data in the lists."], BarCharts`Private`numberQ[
         Pattern[BarCharts`Private`x, 
          Blank[]]] := NumberQ[
         N[BarCharts`Private`x]], BarCharts`Private`orient = Vertical, 
       TagSet[BarCharts`BarSpacing, 
        MessageName[BarCharts`BarSpacing, "usage"], 
        "BarSpacing is an option for bar charts that determines the fraction \
of the bar width to space the bars in a group of bars."], 
       TagSet[BarCharts`BarGroupSpacing, 
        MessageName[BarCharts`BarGroupSpacing, "usage"], 
        "BarGroupSpacing is an option for BarChart that determines the \
spacing between groups of bars."], 
       TagSet[BarCharts`BarLabels, 
        MessageName[BarCharts`BarLabels, "usage"], 
        "BarLabels is an option for BarChart, StackedBarChart, and \
PercentileBarChart, that allows a label to be placed at the tick mark for \
each bar (or group of bars for multiple data sets). Labels are specified in a \
list."], 
       TagSet[BarCharts`BarOrientation, 
        MessageName[BarCharts`BarOrientation, "usage"], 
        "BarOrientation is an option for BarChart that determines whether the \
bars are oriented vertically or horizontally."], 
       BarCharts`GeneralizedBarChart[
         Pattern[BarCharts`Private`idata, 
          Repeated[{
            Repeated[{
              PatternTest[
               Blank[], BarCharts`Private`numberQ], 
              PatternTest[
               Blank[], BarCharts`Private`numberQ], 
              PatternTest[
               Blank[], BarCharts`Private`numberQ]}]}]], 
         PatternTest[
          Pattern[BarCharts`Private`opts, 
           BlankNullSequence[]], OptionQ]] := 
       BarCharts`GeneralizedBarChart[{BarCharts`Private`idata}, 
         BarCharts`Private`opts], BarCharts`GeneralizedBarChart[
         Pattern[BarCharts`Private`idata, {
           Repeated[{
             Repeated[{
               PatternTest[
                Blank[], BarCharts`Private`numberQ], 
               PatternTest[
                Blank[], BarCharts`Private`numberQ], 
               PatternTest[
                Blank[], BarCharts`Private`numberQ]}]}]}], 
         PatternTest[
          Pattern[BarCharts`Private`opts, 
           BlankNullSequence[]], OptionQ]] := 
       Module[{BarCharts`Private`data = BarCharts`Private`idata, 
          BarCharts`Private`bsty, BarCharts`Private`val, 
          BarCharts`Private`vpos, BarCharts`Private`unob, 
          BarCharts`Private`edge, BarCharts`Private`esty, 
          BarCharts`Private`bsf, BarCharts`Private`orient, 
          BarCharts`Private`ln = Length[BarCharts`Private`idata], 
          BarCharts`Private`lns = Map[Length, BarCharts`Private`idata], 
          BarCharts`Private`bars, BarCharts`Private`disp, 
          BarCharts`Private`pr, 
          BarCharts`Private`origopts}, {
           BarCharts`Private`bsty, BarCharts`Private`val, 
            BarCharts`Private`edge, BarCharts`Private`esty, 
            BarCharts`Private`orient, BarCharts`Private`pr} = 
          ReplaceAll[{
            BarCharts`BarStyle, BarCharts`BarValues, BarCharts`BarEdges, 
             BarCharts`BarEdgeStyle, BarCharts`BarOrientation, PlotRange}, 
            Flatten[{BarCharts`Private`opts, 
              Options[BarCharts`GeneralizedBarChart]}]]; 
         BarCharts`Private`origopts = FilterRules[
            Flatten[{BarCharts`Private`opts, 
              Options[BarCharts`GeneralizedBarChart]}], {DisplayFunction}]; 
         BarCharts`Private`gopts = FilterRules[{BarCharts`Private`opts, 
             Options[BarCharts`GeneralizedBarChart]}, 
            Options[Graphics]]; If[
           And[
           BarCharts`Private`bsty =!= Automatic, BarCharts`Private`bsty =!= 
            None, Head[BarCharts`Private`bsty] =!= List, 
            Not[
             MatchQ[BarCharts`Private`bsty, 
              Alternatives[
              Hue, RGBColor, GrayLevel, CMYKColor, Opacity, Directive][
               BlankSequence[]]]]], BarCharts`Private`bsty = Apply[Join, 
             Map[BarCharts`Private`bsty[
               Part[#, 2]]& , BarCharts`Private`data, {2}]], 
           BarCharts`Private`bsty = 
           BarCharts`Private`barcoloring[
            BarCharts`Private`bsty, BarCharts`Private`ln, 
             BarCharts`Private`lns]]; If[
           TrueQ[BarCharts`Private`edge], 
           If[
           BarCharts`Private`ln === 1, BarCharts`Private`esty = 
            BarCharts`Private`CycleValues[BarCharts`Private`esty, 
              Length[
               First[BarCharts`Private`data]]], BarCharts`Private`esty = 
            Apply[Join, 
              MapThread[Table[#, {#2}]& , {
                BarCharts`Private`CycleValues[
                BarCharts`Private`esty, BarCharts`Private`ln], 
                BarCharts`Private`lns}]]], BarCharts`Private`esty = None]; 
         If[
           Not[
            MemberQ[{Horizontal, Vertical}, BarCharts`Private`orient]], 
           Message[
             MessageName[BarCharts`GeneralizedBarChart, "badorient"], 
             BarCharts`Private`orient]; BarCharts`Private`orient = Vertical]; 
         BarCharts`Private`val = TrueQ[BarCharts`Private`val]; 
         BarCharts`Private`vpos = 0.05; 
         BarCharts`Private`data = Flatten[BarCharts`Private`data, 1]; 
         BarCharts`Private`bars = Map[
            BarCharts`Private`barcoords[BarCharts`Private`orient], 
            BarCharts`Private`data]; If[BarCharts`Private`val, 
           Show[
            BarCharts`Private`RectanglePlot[
            BarCharts`Private`bars, BarCharts`Private`RectangleStyle -> 
             BarCharts`Private`bsty, BarCharts`Private`EdgeStyle -> 
             BarCharts`Private`esty, DisplayFunction -> Identity], 
            Graphics[
             Map[
              BarCharts`Private`varcoords[
              BarCharts`Private`orient, BarCharts`Private`vpos, #& ], 
              BarCharts`Private`data]], 
            If[
            BarCharts`Private`pr === Automatic, PlotRange -> All, PlotRange -> 
             BarCharts`Private`pr], BarCharts`Private`origopts, 
            BarCharts`Private`gopts], 
           BarCharts`Private`RectanglePlot[
           BarCharts`Private`bars, BarCharts`Private`RectangleStyle -> 
            BarCharts`Private`bsty, BarCharts`Private`EdgeStyle -> 
            BarCharts`Private`esty, BarCharts`Private`ObscuredFront -> 
            BarCharts`Private`unob, BarCharts`Private`gopts]]], 
       BarCharts`GeneralizedBarChart[{}, 
         Pattern[BarCharts`Private`opts, 
          BlankNullSequence[]]] := Show[
         Graphics[{}, 
          FilterRules[{BarCharts`Private`opts, 
            Options[BarCharts`GeneralizedBarChart]}, 
           Options[Graphics]]]], 
       Options[BarCharts`GeneralizedBarChart] := {
        AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> 
         True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, 
         Background -> None, BarCharts`BarEdges -> True, 
         BarCharts`BarEdgeStyle -> Opacity[0.5], BarCharts`BarOrientation -> 
         Vertical, BarCharts`BarStyle -> Automatic, BarCharts`BarValues -> 
         False, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> 
         Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> 
         False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic,
          FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, 
         ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, 
         LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> 
         All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, 
         PlotRegion -> Automatic, PreserveImageOptions -> Automatic, 
         Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, 
         TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> 
         TraditionalForm}, 
       TagSet[BarCharts`GeneralizedBarChart, 
        MessageName[BarCharts`GeneralizedBarChart, "badorient"], 
        "The value given for BarOrientation is invalid; please use Horizontal \
or Vertical. The chart will be generated with Vertical."], 
       TagSet[BarCharts`GeneralizedBarChart, 
        MessageName[BarCharts`GeneralizedBarChart, "usage"], 
        "\!\(\*RowBox[{\"GeneralizedBarChart\", \"[\", RowBox[{\"{\", \
RowBox[{RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"pos\", \"TI\"], \
StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"height\", \"TI\"], \
StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"width\", \"TI\"], \
StyleBox[\"1\", \"TR\"]]}], \"}\"}], \",\", RowBox[{\"{\", \
RowBox[{SubscriptBox[StyleBox[\"pos\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\
\", SubscriptBox[StyleBox[\"height\", \"TI\"], StyleBox[\"2\", \"TR\"]], \
\",\", SubscriptBox[StyleBox[\"width\", \"TI\"], StyleBox[\"2\", \"TR\"]]}], \
\"}\"}], \",\", RowBox[{StyleBox[\"\[Ellipsis]\", \"TR\"], RowBox[{\"}\", \"]\
\"}]}]}]}]}]\) generates a bar chart with the bars at the given positions, \
and with given heights and widths.\n\!\(\*RowBox[{\"GeneralizedBarChart\", \
\"[\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"list\", \"TI\"], \
StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"list\", \"TI\"], \
StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \
StyleBox[\"}\", \"TR\"]}], \"]\"}]\) generates a bar chart from lists of \
data."], 
       TagSet[BarCharts`BarStyle, 
        MessageName[BarCharts`BarStyle, "usage"], 
        "BarStyle is an option for bar charts that determines the default \
style for the bars. "], 
       TagSet[BarCharts`BarValues, 
        MessageName[BarCharts`BarValues, "usage"], 
        "BarValues is an option for BarChart and GeneralizedBarChart that \
allows the length of the bar to be displayed above each bar."], 
       TagSet[BarCharts`BarEdges, 
        MessageName[BarCharts`BarEdges, "usage"], 
        "BarEdges is an option for bar charts that determines whether edges \
are to be drawn around the bars."], 
       TagSet[BarCharts`BarEdgeStyle, 
        MessageName[BarCharts`BarEdgeStyle, "usage"], 
        "BarEdgeStyle is an option for bar charts that determines the style \
for the edges."], Attributes[PlotRange] = {ReadProtected}, 
       BarCharts`Private`gopts = {
        Frame -> True, FrameLabel -> {"Product Sales", "Qty"}, 
         ImageSize -> {200, 200}, 
         Ticks -> {{{1, "Product 1", 0}, {2, "Product 2", 0}, {
            3, "Product 3", 0}}, Automatic}, 
         AxesOrigin -> {0.3999999999999999, 0}, 
         PlotRange -> {{0.3999999999999999, 3.6}, All}, 
         FrameTicks -> {{{1, "Product 1", 0}, {2, "Product 2", 0}, {
            3, "Product 3", 0}}, Automatic}, AlignmentPoint -> Center, 
         AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> None, 
         AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, 
         BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> 
         Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> 
         False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic,
          FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, 
         ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, 
         LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> 
         All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, 
         PlotRegion -> Automatic, PreserveImageOptions -> Automatic, 
         Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, 
         TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> 
         TraditionalForm, AlignmentPoint -> Center, AspectRatio -> 
         GoldenRatio^(-1), Axes -> True, AxesLabel -> None, AxesOrigin -> 
         Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> 
         Automatic, BaseStyle -> {}, ColorOutput -> Automatic, 
         ContentSelectable -> Automatic, Epilog -> {}, Frame -> False, 
         FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, 
         FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, 
         ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, 
         LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> 
         All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, 
         PlotRegion -> Automatic, PreserveImageOptions -> Automatic, 
         Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, 
         TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> 
         TraditionalForm}, $DisplayFunction = Identity, 
       BarCharts`Private`barcoloring[Automatic, 1, 
         Blank[]] := {
         Hue[0.67, 0.45, 0.65]}, BarCharts`Private`barcoloring[Automatic, 
         Pattern[BarCharts`Private`ln, 
          Blank[]], 
         Pattern[BarCharts`Private`lns, 
          Blank[]]] := Apply[Join, 
         MapThread[Table[#, {#2}]& , {
           Table[
            Hue[
             FractionalPart[
             0.67 + (2. (BarCharts`Private`i - 1))/GoldenRatio], 0.45, 
             0.65], {BarCharts`Private`i, 1, BarCharts`Private`ln}], 
           BarCharts`Private`lns}]], BarCharts`Private`barcoloring[
         Pattern[BarCharts`Private`bsty, 
          Blank[]], 1, 
         Pattern[BarCharts`Private`lns, 
          Blank[]]] := BarCharts`Private`CycleValues[BarCharts`Private`bsty, 
         First[BarCharts`Private`lns]], BarCharts`Private`barcoloring[
         Pattern[BarCharts`Private`bsty, 
          Blank[]], 
         Pattern[BarCharts`Private`ln, 
          Blank[]], 
         Pattern[BarCharts`Private`lns, 
          Blank[]]] := Apply[Join, 
         MapThread[Table[#, {#2}]& , {
           BarCharts`Private`CycleValues[
           BarCharts`Private`bsty, BarCharts`Private`ln], 
           BarCharts`Private`lns}]], BarCharts`Private`CycleValues[{}, 
         Blank[]] := {}, BarCharts`Private`CycleValues[
         Pattern[BarCharts`Private`list, 
          Blank[List]], 
         Pattern[BarCharts`Private`n, 
          Blank[Integer]]] := 
       Module[{BarCharts`Private`hold = BarCharts`Private`list}, 
         While[Length[BarCharts`Private`hold] < BarCharts`Private`n, 
           BarCharts`Private`hold = 
           Join[BarCharts`Private`hold, BarCharts`Private`hold]]; ReplaceAll[
           Take[BarCharts`Private`hold, BarCharts`Private`n], None -> {}]], 
       BarCharts`Private`CycleValues[
         Pattern[BarCharts`Private`item, 
          Blank[]], 
         Pattern[BarCharts`Private`n, 
          Blank[]]] := 
       BarCharts`Private`CycleValues[{BarCharts`Private`item}, 
         BarCharts`Private`n], BarCharts`Private`barcoords[Horizontal][{
          Pattern[BarCharts`Private`pos, 
           Blank[]], 
          Pattern[BarCharts`Private`len, 
           Blank[]], 
          Pattern[BarCharts`Private`wid, 
           Blank[]]}] := {{
         0, BarCharts`Private`pos - BarCharts`Private`wid/2}, {
         BarCharts`Private`len, BarCharts`Private`pos + 
          BarCharts`Private`wid/2}}, BarCharts`Private`barcoords[Vertical][{
          Pattern[BarCharts`Private`pos, 
           Blank[]], 
          Pattern[BarCharts`Private`len, 
           Blank[]], 
          Pattern[BarCharts`Private`wid, 
           Blank[]]}] := {{
         BarCharts`Private`pos - BarCharts`Private`wid/2, 0}, {
         BarCharts`Private`pos + BarCharts`Private`wid/2, 
          BarCharts`Private`len}}, BarCharts`Private`RectanglePlot[
         Pattern[BarCharts`Private`boxes, {
           Repeated[{{
              PatternTest[
               Blank[], BarCharts`Private`numberQ], 
              PatternTest[
               Blank[], BarCharts`Private`numberQ]}, {
              PatternTest[
               Blank[], BarCharts`Private`numberQ], 
              PatternTest[
               Blank[], BarCharts`Private`numberQ]}}]}], 
         PatternTest[
          Pattern[BarCharts`Private`opts, 
           BlankNullSequence[]], OptionQ]] := 
       Module[{BarCharts`Private`ln = Length[BarCharts`Private`boxes], 
          BarCharts`Private`bstyle, BarCharts`Private`estyle, 
          BarCharts`Private`gopts, 
          BarCharts`Private`sort}, {
           BarCharts`Private`bstyle, BarCharts`Private`estyle, 
            BarCharts`Private`sort} = 
          ReplaceAll[{
            BarCharts`Private`RectangleStyle, BarCharts`Private`EdgeStyle, 
             BarCharts`Private`ObscuredFront}, 
            Flatten[{BarCharts`Private`opts, 
              Options[BarCharts`Private`RectanglePlot]}]]; 
         BarCharts`Private`gopts = FilterRules[{BarCharts`Private`opts, 
             Options[BarCharts`Private`RectanglePlot]}, 
            Options[Graphics]]; 
         If[BarCharts`Private`bstyle === Automatic, BarCharts`Private`bstyle = 
           Map[Hue, (0.6 Range[0, BarCharts`Private`ln - 1])/(
             BarCharts`Private`ln - 1)]]; 
         If[BarCharts`Private`bstyle === {}, BarCharts`Private`bstyle = {{}}]; 
         If[BarCharts`Private`bstyle === None, 
           BarCharts`Private`bstyle = {{}}]; 
         If[BarCharts`Private`estyle === Automatic, 
           BarCharts`Private`estyle = {
             GrayLevel[0]}]; 
         If[BarCharts`Private`estyle === {}, BarCharts`Private`estyle = {{}}]; 
         If[BarCharts`Private`estyle === None, 
           BarCharts`Private`estyle = {{}}]; 
         BarCharts`Private`bstyle = 
          BarCharts`Private`CycleValues[
           BarCharts`Private`bstyle, BarCharts`Private`ln]; 
         BarCharts`Private`estyle = 
          BarCharts`Private`CycleValues[
           BarCharts`Private`estyle, BarCharts`Private`ln]; 
         BarCharts`Private`recs = Table[{
             Part[BarCharts`Private`bstyle, BarCharts`Private`i], 
             EdgeForm[
              Part[BarCharts`Private`estyle, BarCharts`Private`i]], 
             Apply[Rectangle, 
              Part[BarCharts`Private`boxes, BarCharts`Private`i]]}, {
            BarCharts`Private`i, 
             Length[BarCharts`Private`boxes]}]; Show[
           Graphics[BarCharts`Private`recs], BarCharts`Private`gopts]], 
       BarCharts`Private`RectanglePlot[
         Pattern[BarCharts`Private`boxes, {
           Repeated[{
             PatternTest[
              Blank[], BarCharts`Private`numberQ], 
             PatternTest[
              Blank[], BarCharts`Private`numberQ]}]}], 
         Pattern[BarCharts`Private`opts, 
          BlankNullSequence[]]] := BarCharts`Private`RectanglePlot[
         Map[{#, # + 1}& , BarCharts`Private`boxes], BarCharts`Private`opts], 
       Options[BarCharts`Private`RectanglePlot] := {
        BarCharts`Private`RectangleStyle -> Automatic, 
         BarCharts`Private`EdgeStyle -> Automatic, 
         BarCharts`Private`ObscuredFront -> False, AlignmentPoint -> Center, 
         AspectRatio -> GoldenRatio^(-1), Axes -> False, AxesLabel -> None, 
         AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, 
         BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> 
         Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> 
         False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic,
          FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, 
         ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, 
         LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> 
         All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, 
         PlotRegion -> Automatic, PreserveImageOptions -> Automatic, 
         Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, 
         TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> 
         TraditionalForm}, BarCharts`Private`recs = {{
          Directive[
           RGBColor[1, 1, 0], 
           Opacity[0.5]], 
          EdgeForm[
           Opacity[0.5]], 
          Rectangle[{0.615, 0}, {1.385, 50}]}, {
          Directive[
           RGBColor[1, 1, 0], 
           Opacity[0.5]], 
          EdgeForm[
           Opacity[0.5]], 
          Rectangle[{1.615, 0}, {2.385, 100}]}, {
          Directive[
           RGBColor[1, 1, 0], 
           Opacity[0.5]], 
          EdgeForm[
           Opacity[0.5]], 
          Rectangle[{2.615, 0}, {3.385, 100}]}}, 
       BarCharts`Private`varcoords[Horizontal, 
         Pattern[BarCharts`Private`offset, 
          Blank[]], 
         Pattern[BarCharts`Private`format, 
          Blank[]]][{
          Pattern[BarCharts`Private`pos, 
           Blank[]], 
          Pattern[BarCharts`Private`len, 
           Blank[]], 
          Pattern[BarCharts`Private`wid, 
           Blank[]]}] := Text[
         BarCharts`Private`format[BarCharts`Private`len], 
         Scaled[{ReplaceAll[
             Sign[BarCharts`Private`len], 0 -> 1] BarCharts`Private`offset, 
           0}, {BarCharts`Private`len, BarCharts`Private`pos}]], 
       BarCharts`Private`varcoords[Vertical, 
         Pattern[BarCharts`Private`offset, 
          Blank[]], 
         Pattern[BarCharts`Private`format, 
          Blank[]]][{
          Pattern[BarCharts`Private`pos, 
           Blank[]], 
          Pattern[BarCharts`Private`len, 
           Blank[]], 
          Pattern[BarCharts`Private`wid, 
           Blank[]]}] := Text[
         BarCharts`Private`format[BarCharts`Private`len], 
         Scaled[{0, ReplaceAll[
             Sign[BarCharts`Private`len], 0 -> 1] BarCharts`Private`offset}, {
          BarCharts`Private`pos, BarCharts`Private`len}]]}; 
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    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
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   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
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Cell[TextData[{
 StyleBox["Thank You!", "Subsection"],
 "\n\nThank you for trying this demonstration. Did you find it useful? Did it \
help you solve a problem? If so, please email us and let us know how you used \
it to solve your problem.\n\nWe are looking for ideas for new demonstrations \
to help people solve real problems. If you have an idea for a demonstration \
or would like to sponsor an application, don't hesitate to contact us via \
email at analyst@10squaredcorp.com or phone (404) 271-1907.\n\nThis \
demonstration is provided courtesy of ",
 StyleBox["10 Squared Corporation",
  FontWeight->"Bold"],
 ", an Atlanta, Georgia based consulting firm. "
}], "Text",
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