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# Exam 1 2009_2010 w answers - University of Pittsburgh...

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University of Pittsburgh BUSQOM 0050 Quantitative Methods Exam 1 Fall 2009 - 2010

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R. E. Wendell 2
1. Basic Linear Optimization Modeling 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. P ROFIT FOR E ACH P RODUCT Product 1 Product 2 Product 3 Plant 1 \$10.00/Box \$9.00/lb \$8.00/Unit Plant 2 \$7.75/Box \$10.50/lb \$ 8.50/Unit The situation concerning capacities and production requirements is shown in the tables below. Plant 1 Labor Machine unfinished Product 1 2 hours/box 3 hours/box finished Product 1 unfinished Product 2 3 hours/lb. 1 hour/lb. finished Product 2 unfinished Product 3 2 hours/unit 2 hours/unit finished Product 3 Labor Capacity 300 hours Machine Capacity 400 hours Plant 2 Labor Machine unfinished Product 1 6 hours/box 4 hours/box finished Product 1 unfinished Product 2 4 hours/lb. 3 hours/lb. finished Product 2 unfinished Product 3 2 hours/unit 5 hours/unit finished Product 3 Labor Machine Capacity 3

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Capacity 500 hours 450 hours The decision variables for the problem are: B 1 = Boxes of Product 1 made at Plant 1 B 2 = Boxes of Product 1 made at Plant 2 L 1 = Pounds of Product 2 made at Plant 1 L 2 = Pounds of Product 2 made at Plant 2 U 1 = Units of Product 3 made at Plant 1 U 2 = Units of Product 3 made at Plant 2 Using these variables, and only these variables, formulate a linear optimization model to maximize profit. 4
Solution to 1: (20 pts) The algebraic formulation is: Max 10.00B 1 +7.75B 2 +9.00L 1 + 10.50L 2 + 8.00U 1 + 8.50U 2 s.t.

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Exam 1 2009_2010 w answers - University of Pittsburgh...

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