Chapter 4 homework

Chapter 4 homework - Linear Programming Applications in...

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Linear Programming Applications in Marketing, Finance and Operations Management Chapter 4 Homework Solutions Problem 1, 2a, 3, 4abc, 8, 11, 14ab, 17abc, 18 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. 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. 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 1 + 0.35 x 2 100 Dept. A 0.30 x 1 + 0.20 x 2 36 Dept. B 0.20 x 1 + 0.50 x 2 50 Dept. C x 1 , x 2 0 Solution: x 1 = 77.89, x 2 = 63.16 Profit = 3284.21 3. x 1 = $ automobile loans x 2 = $ furniture loans x 3 = $ other secured loans
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Chapter 4 x 4 = $ signature loans x 5 = $ "risk free" securities Max 0.08 x 1 + 0.10 x 2 + 0.11 x 3 + 0.12 x 4 + 0.09 x 5 s.t. x 5 600,000 [1] x 4 0.10( x 1 + x 2 + x 3 + x 4 ) or -0.10 x 1 - 0.10 x 2 - 0.10 x 3 + 0.90 x 4 0 [2] x 2 + x 3 x 1 or - x 1 + x 2 + x 3 0 [3] x 3 + x 4 x 5 or + x 3 + x
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Chapter 4 homework - Linear Programming Applications in...

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