Problem: Costal Cup Company wants to determine how many cases of large and small cups should be produced per day in order to maximize profit given the labor and material constraints. The unit profit value for large cups is $35 per case, for small cups the unit profit value is $30 per case. There are 120 hours of labor, 2000 units of resin material, and 325 units of packaging material available per day. Each case of large cups requires .75 hours of labor, 16 units of resin material, and 2.5 units of packaging material to produce and package, each case of small cups requires 1 hour of labor and 11 units of resin material and 2 units of packaging material to produce and package
1. Formulate a linear programming model for this problem to determine how many cases of large and small cups should be produced in order to maximize the total profit.
2. Solve this problem by using the graphing method OR by using Excel Solver.
3. What is the optimal solution?
Note: Instructions for how to add and use the Solver Add-in are located in the Week 1 Instructional Material: Lecture: Linear Programming Modeling Using Excel.
Lecture: Linear Programming Modeling Using Excel: Linear Programming Modeling Using Excel We will be using the Solver tool with Excel to create and solve Linear Programming Models. Solver comes with Excel, but may not be added in by default. To Add in Solver Open up an Excel worksheet. Select the ‘Data’ tab at the top of the worksheet, look to the right, if there is NOT a Solver option then do the following: For Office 2013 Select ‘File’, select ‘Options’, select ‘Add-Ins’, next to ‘Excel Add-ins’, select ‘Go’. From the ‘Add-Ins’ screen, select ‘Solver Add-in’, ‘Analysis ToolPak’, and ‘Analysis ToolPak-VBA’, and ‘OK’. For Office 2007 Select the ‘Office’ button (upper left of screen), select ‘Excel Options’, and select ‘Add-Ins’. Select ‘Go’ next to ‘Solver Add-ins’. Select ‘Solver Add-in’, ‘Analysis ToolPak’, and ‘Analysis ToolPak-VBA’, and ‘OK’.
