Exam 3 2009_2010 w answers

Exam 3 2009_2010 w answers - University of Pittsburgh...

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University of Pittsburgh BUSQOM 0050 Quantitative Methods Fall 2009 EXAM 3 R. E. Wendell
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1. Product Mix The Monet Company produces four types of picture frames, which we label 1, 2, 3, and 4. The four types of frames differ with respect to size, shape, and materials used. Each type requires a certain amount of skilled labor, metal, and glass, as shown in Table 1. This table also lists the unit selling price Monet charges for each type of frame. During the coming week, Monet can purchase up to 4000 hours of skilled labor, 6000 ounces of metal, and 10,000 ounces of glass. The unit costs are $4.00 per labor hour, $2.00 per ounce of metal, and $1.00 per ounce of glass. Also, market constraints are such that it is impossible to sell more than 1000 type 1 frames, 2000 type 2 frames, 500 type 3 frames, and 1000 type 4 frames. The company wants to maximize its weekly profit. Let X 1 = # of frames of type 1 to produce next week. X 2 = # of frames of type 2 to produce next week. X 3 = # of frames of type 3 to produce next week. X 4 = # of frames of type 4 to produce next week. Using only these variables, formulate a linear optimization model to maximize Monet's profits. Please indicate how you computed your objective function coefficients. Table 1 Skilled Labor hours/unit Metal oz/unit Glass oz/unit Selling Price $/unit Frame 1 2 4 6 $28 Frame 2 1 2 2 $12 Frame 3 3 1 1 $29 Frame 4 2 2 2 $21 2
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Solution: $ Profit/unit frame 1 = (28-4*2-2*4-1*6 = 6 $ Profit/unit frame 2 = (12-4*1-2*2-1*2 = 2 $ Profit/unit frame 3 = (29-4*3-2*1-1*1 = 14 $ Profit/unit frame 4 = (21-4*2-2*2-1*2 = 7 Model is: Max 6x1+2x2+14x3+7x4 St 2x1+1x2+3x3+2x4 <= 4000 4x1+2x2+1x3+2x4 <= 6000 6x1+2x2+1x3+2x4 <= 10,000 x1 <= 1000 x2 <= 2000 x3 <= 500 x4 <= 1000 x1, x2, x3, x4 >= 0 3
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2. Multiplant Company The Multiplant Company has two plants, each of which has the capability for producing three products. The capacity of each plant is limited by the man-hours of labor available and by the amount of machine time available. Suppose that the sales potential is 80 boxes of Product 1, 100 lbs of Product 2, and 200 units of Product 3. The profit, which depends on the plant in which the product is produced, is shown below.
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