CH 03 Assignments

CH 03 Assignments - Revised January 2011 Chapter 03...

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Revised January 2011 Chapter 03 Assignments:  Problem 1 Consider the following linear program: Min 8X + 12Y s.t. 1 X + 3Y 9 2X + 2Y 10 6X + 2Y 18 X, Y 0 a. Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c. Assume that the objective function coefficient for X remains 8, but the objective func- tion coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The Management Scientist computer solution for the linear program in part (a) provides the following objective coefficient range information: Variable Lower Limit Current Value Upper Limit X 4 8 12 Y 8 12 24 How would this objective coefficient range information help you answer parts (b) and(c) prior to resolving the problem?  Problem 2 Refer to the Kelson Sporting Equipment, Inc., make two different types of baseball gloves: a regular model and a catcher’s model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packing and shipping department. The production time requirements and the profit contribution per glove are given in the following table. Production Time (hours) Model Cutting and Sewing Finishing Packing & Shipping Profit per Glove Regular 1 1/2 1/8 $5 Catcher’s 3/2 1/3 1/4 $8
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Letting R= number of regular gloves to produce C= number of catcher’s gloves to produce leads to the following formulation: Max 5 R + 8 C s.t. R + 3/2 C 900 Cutting and sewing 1/2 R + 1/3 C 300 Finishing 1/8 R + 1/4 C 100 Packaging and shipping R, C ≥ 0 The computer solution obtained using The Management Scientist is shown in the following table.
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CH 03 Assignments - Revised January 2011 Chapter 03...

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