Explanation Given Information: The provided given information is: The marketing director of company that manufacture bodybuilding supplements, and you are planning to runs ads in sports illustrated and Muscle and Fitness. The estimate that each ad in Sports illustrated will be read by 600 , 000 people in the target group, while each ad in Muscle and Fitness will read by 300 , 000 . They would like that ad to be read by at least 9 million people in the target group, and plan to place at least 4 ads in sports illustrated and at least 4 ads in Muscle and Fitness during the next year. Sports illustrated quotes $ 3 , 000 per ad, while Muscle and Fitness quotes $ 2 , 000 per ad. Formula used: A common kind of economic application is one that leads to a standard maximization problem involving minimizing cost. The minimum cost that is obtained depends on the constraints is: A s + B t + C u + …… ≥ N . Where N is typically the number of units of required quantity. Calculation: As given, 600 , 000 people in the target group, while each ad in Muscle and Fitness will read by 300 , 000 . They would like ad to be read by at least 9 million people in the target group, and plan to place at least 4 ads in sports illustrated and at least 4 ads in Muscle and Fitness during the next year. Sports illustrated quotes $ 3 , 000 per ad, while Muscle and Fitness quotes $ 2 , 000 per ad. Let x is full-page ads in sports illustrated, y is full page in Muscle and Fitness. According to the above information the equation is as: Minimize c = 3 s + 2 t Subject to 600 s + 300 t ≥ 9 , 000 s ≥ 3 , t ≥ 4 s ≥ 0 , t ≥ 0 , u ≥ 0 The matrix is as: [ 600 300 9000 1 0 3 0 1 4 3 2 0 ] Transpose of above matrix is: [ 600 1 0 300 0 1 9000 3 4 3 2 0 ] Solving it by dual problem solution as: Maximize p = 9000x+3y+4z Subject to 600 x + y ≤ 3 300 x + z ≤ 2 x ≥ 0 , y ≥ 0 , z ≥ 0 Set up the initial tableau as: x y s t u p

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ISBN: 9781337291262

Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

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Chapter 5.5, Problem 38E

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To calculate: The number of ads should be placed in each magazine to satisfy the requirement at a minimum cost.

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Chapter 5.5, Problem 37E

Chapter 5.5, Problem 39E

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The number of ads should be placed in each magazine to satisfy the requirement at a minimum cost.

Solution Summary: The author calculates the number of ads to be placed in each magazine to satisfy the requirement at a minimum cost.

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To calculate: The number of ads should be placed in each magazine to satisfy the requirement at a minimum cost.

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Chapter 5 Solutions