# HW1 - P 2 Identify for each LP which of the following cases...

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1. Homework for IEOR162 Linear Programming Semester: Fall 2010 Instructor: Dr. Sarah Drewes Due to: Tue, September 14, 2010 (at the beginning of class) P 1 A company produces two types of waistbelts: type A and type B. A is of better quality than B. The pro±t of type A is 2 Dollars and the pro±t of type B is 1.5 Dollars. The time needed to produce one belt is 2 time units for type A and 1 time unit for type B. Each day, there are 1000 time units for disposition. The raw material (leather) that can be used each day su²ces to produce 800 belts (no matter which type). Furthermore, 400 belt buckles of type A and 700 belt buckles for type B can be used per day. a) Write down the optimization model which determines the daily production of belts of type A and type B that maximizes the daily pro±t. b) Solve the problem graphically. c) Which are the binding constraints?

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Unformatted text preview: P 2 Identify for each LP, which of the following cases apply: 1. The LP has a unique optimal solution. 2. The LP has multiple optimal solutions. 3. The LP is infeasible. 4. The LP is unbounded. 1 a) max z = x 1 + x 2 s.t. x 1 + x 2 ≤ 4 x 1-x 2 ≥ 5 x 1 , x 2 ≥ b) max z = 4 x 1 + x 2 s.t. 8 x 1 + 2 x 2 ≤ 16 5 x 1 + 2 x 2 ≤ 12 x 1 , x 2 ≥ c) max z =-x 1 + 3 x 2 s.t. x 1-x 2 ≤ 4 x 1 + 2 x 2 ≥ 4 x 1 , x 2 ≥ d) max z = 3 x 1 + x 2 s.t. 2 x 1 + x 2 ≤ 6 x 1 + 3 x 2 ≤ 9 x 1 , x 2 ≥ P 3 Suppose an LP has bounded feasible region (the feasible region is not unbounded). Why can you Fnd the optimal solution of the LP (without an isoproFt or isocost line) by checking the z-values at each extreme point of the feasible region? Why might this fail if the feasible region is unbounded? 2...
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HW1 - P 2 Identify for each LP which of the following cases...

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