# hw2 - IEOR 162 LINEAR PROGRAMMING(FALL 04 HOMEWORK 2...

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IEOR 162 LINEAR PROGRAMMING (FALL 04) HOMEWORK 2 SOLUTIONS 3.1.1. max z = 30x 1 + 100x 2 s.t. x 1 + x 2 7 (Land Constraint) 4x 1 + 10x 2 40(Labor Constraint) 10x 1 30(Govt. Constraint) x 1 0, x 2 0 3.1.2 a. No, government constraint is violated. b. No; Labor constraint is not satisfied. c. No, x 2 0 is not satisfied. d. Yes, all constraints and sign restrictions are satisfied. 3.2.1. EF is 4x 1 + 10x 2 = 40, CD is x 1 = 3, and AB is x 1 + x 2 = 7. The feasible region is bounded by ACGH. The dotted line in graph is isoprofit line 30x 1 + 100x 2 = 120. Point G is optimal. At G the constraints 10x 1 30 and 4x 1 + 10x 2 40 are binding. Thus optimal solution has x 1 = 3, x 2 = 2.8 and z = 30(3) + 100(2.8) = 370.

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3.2.3. x 1 = Number of hours of Process 1 and x 2 = Number of hours of Process 2. Then the appropriate LP is min z = 4x 1 + x 2 s.t. 3x 1 + x 2 10 (A constraint) x 1 + x 2 5 (B constraint)
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hw2 - IEOR 162 LINEAR PROGRAMMING(FALL 04 HOMEWORK 2...

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