Ch4 Solutions 1-7

# Ch4 Solutions 1-7 - Chapter 4 Linear Programming...

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Chapter 4 Linear Programming Applications in Marketing, Finance and Operations Management Note that the solution and the interpretation of the solution will require the use of as Microsoft Excel 's Solver. 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 0 Max 50% Radio 0.9 T - 0.1 R - 0.1 N 0 Min 10% TV T , R , N , 0 Budget \$ Solution: T = 4 \$8,000 R = 14 4,200 N = 10 6,000 \$18,200 Audience = 1,052,000. OPTIMAL SOLUTION Optimal Objective Value 1052000.00000 Variable Value Reduced Cost T 4.00000 0.00000 R 14.00000 0.00000 N 10.00000 11826.08695 Constraint Slack/Surplus Dual Value 1 0.00000 51.30430 2 6.00000 0.00000 3 6.00000 0.00000

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Chapter 4 4 0.00000 11826.08695 5 0.00000 5217.39130 6 1.20000 0.00000 Objective Allowable Allowable Coefficient Increase Decrease 100000.00000 20000.00000 118000.00000 18000.00000 Infinite 3000.00000 40000.00000 Infinite 11826.08695 RHS Allowable Allowable Value Increase Decrease 18200.00000 13800.00000 3450.00000 10.00000 Infinite 6.00000 20.00000 Infinite 6.00000 10.00000 2.93600 10.00000 0.00000 2.93617 8.05000 0.00000 1.20000 Infinite b. The dual value 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. 2. a. Let x 1 = units of product 1 produced x 2 = units of product 2 produced Max 30 x 1 + 15 x 2 s.t. x
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## This note was uploaded on 05/01/2011 for the course BUS 220 taught by Professor Drexel during the Fall '08 term at SUNY Stony Brook.

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Ch4 Solutions 1-7 - Chapter 4 Linear Programming...

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