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IEOR162_hw03

# IEOR162_hw03 - IEOR 162 Spring 2010 Suggested Solution to...

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IEOR 162, Spring 2010 Suggested Solution to Homework 03 Problem 3.3.2 The graphical solution of this problem is shown in Figure 1. The feasible region is the shaded zone. The dotted line is the isoprofit line with (4 , 1) as the improving direction. As shown in this figure, all points between A = ( 4 3 , 8 3 ) and B = (2 , 0) are optimal. Therefore, this problem has multiple optimal solutions. 5x + 2x = 12 8x + 2x = 16 2 1 1 2 x x 1 2 A (4, 1) B Figure 1: Graphical solution of Problem 3.3.2 3x + 5x = 45 3x + 2x = 36 1 2 1 2 x x 1 2 A (-3, -5) B Figure 2: Graphical solution of Problem 3.3.9 Problem 3.3.5 True. An LP is unbounded implies we can push its isoprofit/isocost line as far as we want and still have feasible solution at the line. This implies the feasible region is unbounded. Problem 3.3.6 False. For example, consider max x 1 s.t. x 1 10 . For this LP, the feasible region is unbounded (all real numbers that is no greater than 10, or ( -∞ , 10)), but the optimal solution exists: x 1 = 10 optimizes the LP.

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IEOR162_hw03 - IEOR 162 Spring 2010 Suggested Solution to...

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