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midtermI_sample - Quiz Sample Due Problem 1[20 points Top...

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Quiz Sample Due: February 24, 2009 Problem 1 [20 points] Top Brass Trophy Company makes large championship trophies for youth athletic leagues. They are planning production for fall sports:football and soccer. Each football trophy has a wood base, engraved plaque, and a large brass football on a top, and returns $12. Soccer trophies are similar except that a brass soccer ball is on a top and the unit profit is $9. The football base requires 4-feet board, while the soccer base requires 2-feet board. The company has 1000 brass footballs in stock, 1500 soccer brass balls, 1750 plaques, and 4800 feet of board. Assume that what is produced can be sold. (a) [10 points] Formulate a linear programming model corresponding to maximizing the company’s profit subject to the given resource constraints. (b) [10 points] Write the problem in the standard form Problem 2 [25 points] Solve the following problem by M -method or by the two- phase method. maximize z = 3 x 1 + 2 x 2 3 x 3 subject to 2 x 1 + x 2 + x 3 2 3 x 1 + 4 x 2 + 2 x 3 8 x 1 , x 2 , x 3 0 .
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