MS11 SM04 - Chapter 4 Linear Programming Applications...

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Unformatted text preview: Chapter 4 Linear Programming Applications Learning Objectives 1. Learn about applications of linear programming that have been encountered in practice. 2. Develop an appreciation for the diversity of problems that can be modeled as linear programs. 3. Obtain practice and experience in formulating realistic linear programming models. 4. Understand linear programming applications such as: media selection production scheduling portfolio selection work force assignments financial mix strategy blending problems data envelopment analysis revenue management Note to Instructor The application problems of Chapter 9 have been designed to give the student an understanding and appreciation of the broad range of problems that can be approached by linear programming. While the problems are indicative of the many linear programming applications, they have been kept relatively small in order to ease the student's formulation and solution effort. Each problem will give the student an opportunity to practice formulating an approximate linear programming model. However, the solution and the interpretation of the solution will require the use of a software package such as The Management Scientist , Microsoft Excel 's Solver or LINDO. 4 - 1 Chapter 4 Solutions: 1. a. Let T = number of television spot advertisements R = number of radio advertisements N = number of newspaper advertisements Max 100,000 T + 18,000 R + 40,000 N s.t. 2,000 T + 300 R + 600 N 18,200 Budget T 10 Max TV R 20 Max Radio N 10 Max News-0.5 T + 0.5 R- 0.5 N Max 50% Radio 0.9 T- 0.1 R- 0.1 N Min 10% TV T , R , N , Budget $ Solution: T = 4 $8,000 R = 14 4,200 N = 10 6,000 $18,200 Audience = 1,052,000. This information can be obtained from The Management Scientist as follows. OPTIMAL SOLUTION Objective Function Value = 1052000.000 Variable Value Reduced Costs -------------- --------------- ------------------ T 4.000 0.000 R 14.000 0.000 N 10.000 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 51.304 2 6.000 0.000 3 6.000 0.000 4 0.000 11826.087 5 0.000 5217.391 6 1.200 0.000 OBJECTIVE COEFFICIENT RANGES 4 - 2 Linear Programming Applications Variable Lower Limit Current Value Upper Limit------------ --------------- --------------- --------------- T -18000.000 100000.000 120000.000 R 15000.000 18000.000 No Upper Limit N 28173.913 40000.000 No Upper Limit RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit------------ --------------- --------------- --------------- 1 14750.000 18200.000 31999.996 2 4.000 10.000 No Upper Limit 3 14.000 20.000 No Upper Limit 4 0.000 10.000 12.339 5 -8.050 0.000 2.936 6 No Lower Limit 0.000 1.200 b. The dual price for the budget constraint is 51.30. Thus, a $100 increase in budget should provide an increase in audience coverage of approximately 5,130. The right-hand-side range for the budget constraint will show this interpretation is correct....
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MS11 SM04 - Chapter 4 Linear Programming Applications...

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