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hw4 copy

# hw4 copy - n products you desire and the m pack-ages that...

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CS231: Topics in Combinatorial Algorithms Prof. Suri Homework Assignment 4 Handed Out: Nov. 23 Due: Dec. 2 1. Modern Furniture Inc. produces two types of wooden chairs. Manufacturing chair A requires 2 hours of assembly time and 4 hours of ﬁnishing time. Chair B requires 3 hours to assemble and 3 hours to ﬁnish. Modern estimates that next week 72 hours will be available for assembly and 108 hours for the ﬁnishing operations. The unit proﬁts for Chairs A and B are \$10 and \$9, respectively. If it is estimated that the maximum demand for Chair B is 16, what is the optimal product mix? Formulate a linear programming model and solve it using the graphical method. 2. Suppose you wish to acquire unit quantity of each of the n products, i = 1 , 2 ,...,n . In the market, these are m package deals, j = 1 , 2 ,...,m , that bundle these prod- ucts in various combinations. For instance, one such package might contain one unit each of products 3 , 7 and 15, and cost \$50. Such a package can be speciﬁed as the tuple h (3 , 7 , 15) , \$50 i . Given the list of
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Unformatted text preview: n products you desire, and the m pack-ages that the market oﬀers, formulate a linear program that models the problem of acquiring unit quantity of all n products at the minimum possible total cost . Your solutions may accept fractional packages. (You don’t have to solve the linear program; just formulate it.) 3. An automotive ﬁrm produces 3 types of cars: luxury, midsize, compact. These three types have gasoline mileage of 18, 29, and 38 miles/gallon, respectively. They generate proﬁts of \$600, \$460, and \$320 per car, resp. The estimated demands are 600,00 units for luxury, 800,000 for midsize, and 700,000 for compact. Government regulations require that the average gasoline mileage for the company’s entire line of cars should be at least 30 miles/gallon. Formulate the linear programming model for this problem to maximize the company’s proﬁt. (You do not have to solve the problem; just describe the LP formulation.)...
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