Sample Midterm2_Solution

Sample Midterm2_Solution - ADM 2302 Midterm Exam Problem...

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ADM 2302 Midterm Exam Problem 1 (12 points) Consider the following linear program: Max Z = X 1 – 2X 2 Subject to – 4X 1 + 3X 2 <= 3 X 1 – X 2 <= 3 X 1 , X 2 >= 0 a) Graph the feasible region for the problem. (4 points) b) Is the feasible region unbounded? Explain. (2 points) Yes, cause it is not closed region. It is open on one side. c) Find the optimal solution. (4 points) X1 = 3, X2 = 0 Z = 3 d) Does an unbounded feasible region imply that the optimal solution to the linear program will be unbounded? (2 points) No and this example is a proof. Professor: Rim Jaber Page: 1
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ADM 2302 Midterm Exam Problem 2 (20 points) A large sporting goods store is placing an order for bicycles with its supplier. Four models can be ordered: the adult Open Trail, the adult Citscape, the girl’s Sea Sprite, and the boy’s Trail Blazer. It is assumed that every bike ordered will be sold, and their profits, respectively, are 30, 25, 22, and 20. The LP model should maximize the profit. There are several conditions that the store needs to worry about. One of these is space to hold the inventory. The adult bikes need two feet, but each children’s bike needs only one foot. The store has 500 feet of space. There are 1200 hours of assembly time available. The children’s bikes need 4 hours each; the Open Trail needs 5 hours and the Cityscape needs 6 hours. The store would like to place an order for at least 275 bikes. The problem when formulated as an LP and solved is as follows: Max. Z = 30 X1 +25 X2 + 22 X3 + 20 X4 Subject to C1 2 X1 + 2 X2 + X3 + X4 <= 500 C2 5 X1 + 6 X2 + 4 X3 + 4 X4 <= 1200 C3 X1 + X2 + X3 + X4 >= 275 X1, X2, X3, X4 >= 0 Professor: Rim Jaber Page: 2
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Sample Midterm2_Solution - ADM 2302 Midterm Exam Problem...

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