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IEOR162_hw07 - IEOR 162 Fall 2011 Homework 07 1(Modied from...

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IEOR 162, Fall 2011 Homework 07 1. (Modified from Problem 6.1.4; 17 points) Consider the Dorian Auto problem as below: 1 Dorian Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, Dorian Auto has embarked on an ambitious TV advertising campaign and has decided to purchase 1-minute commercial spots on two types of programs: comedy shows and football games. Each comedy commercial is seen by 7 million high-income women and 2 million high income men. Each football commercial is seen by 2 million high-income women and 12 million high-income men. A 1-minute comedy ad costs $50,000, and a 1-minute football ad costs $100,000. Dorian would like the commercials to be seen by at least 28 million high-income women and 24 million high-income men. Use linear programming to determine how Dorian Auto can meet its advertising requirements at minimum cost. Dorian must decide how many comedy and football ads should be purchased, so the decision variables are x 1 = number of 1-minute comedy ads purchased, and x 2 = number of 1-minute football ads purchased. The LP to be solved is min 50 x 1 + 100 x 2 s.t. 7 x 1 + 2 x 2 28 2 x 1 + 12 x 2 24 x 1 0 , x 2 0 The optimal solution is x * = ( x * 1 , x * 2 ) = (3 . 6 , 1 . 4). The corresponding objective value is z * = 320 (which means $320,000 to spend).
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