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Unformatted text preview: IEOR 162, Spring 2012 Suggested Solution to Homework 02 Problem 1 (Modified from Problems 3.3.5 and 3.3.6) (a) True. An LP is unbounded implies that we can push its isoprofit line as far as we want and still have feasible solution at the line. This implies the feasible region is unbounded. (b) False. For example, consider the LP of maximizing x 1 subject to x 1 ≤ 10. For this LP, the feasible region is unbounded (all real numbers that is no greater than 10 are feasible), but there is an optimal solution: x * 1 = 10 optimizes the LP. Problem 2 (Modified from Problem 3.3.8) The graphical solution of this problem is shown in Figure 1. For each constraint, we associate an arrow indicating the feasible side. From the figure we can see that there is no feasible solution for this problem and thus this problem is infeasible. x - x = 0 x + x = 6 x x- x + x = 3 1 2 2 1 2 1 1 2 Figure 1: Graphical solution for Problem 3.3.8 Another way to see the infeasibility of this problem is to multiply the third constraint by- 1. As it becomes x 1- x 2 ≤ - 3, it is clear that we can not find a pair of x 1 and x 2 such that x 1- x 2 is no less than...
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This note was uploaded on 03/14/2012 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at Berkeley.
- Spring '07