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Assignment 2

# Assignment 2 - the corners were traversed 2 Solve the LP...

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Economics 146 – Fall, 2007 Homework Assignment 2 – due October 25, 2007 Last update: 10/17/07 Instruction: In each of these problems solve means to find all optimal solutions, if any, by the use of the simplex method. 1. Let S be the constraint set given by: 2 x 1 - x 2 12 - x 1 + x 2 3 2 x 1 + 3 x 2 24 and x 1 , x 2 0 Solve the maximization problem given by each of the following objective functions subject to the constraint set S : (a) x 1 + 2 x 2 (b) x 1 + 1 . 5 x 2 (c) x 1 - x 2 Graph the constraint set and mark the corners of the constraint set corresponding to the basic feasible solutions. For each of the three problems give the order in which
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Unformatted text preview: the corners were traversed. 2. Solve the LP problem maximize 3 x 1 + 2 x 2 subject to x 1 + x 2 ≤ 2 2 x 1-x 2 ≥ 6 and x 1 , x 2 ≥ 3. Solve the LP problem maximize 2 x 1 + x 2 + 3 x 3 + 2 x 4 subject to x 1-2 x 2 + x 3-2 x 4 ≤ 12 3 x 1 + 4 x 2-2 x 3 + 5 x 4 ≥ 20 and x 1 , x 2 , x 3 , x 4 ≥ 4. Solve the LP problem maximize x 1 + 5 x 2 + 2 x 3 subject to 4 x 1 + x 2 + 3 x 3 ≤ 6 x 1 + 4 x 2 + 2 x 3 ≥ 8 3 x 1 + 2 x 2 + 6 x 3 ≤ 12 and x 1 , x 2 , x 3 ≥ 1...
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