HW_Solution_Chapter 09_EMSE102-202

HW_Solution_Chapter 09_EMSE102-202 - 1 CHAPTER 9 OR...

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Unformatted text preview: 1 CHAPTER 9 OR SOLUTIONS SECTION 9.2 3. Let x 1 = Units of Product 1 produced x 2 = Units of Product 2 produced y i = 1 if any Product i is produced y i = 0 otherwise Then the appropriate IP is max z = 2x 1 + 5x 2- 10y 1- 20y 2 s.t. 3x 1 + 6x 2 ≤ 120 x 1 ≤ 40y 1 x 2 ≤ 20y 2 x 1 ≥ 0,x 2 ≥ 0, y 1 ,y 2 = 0 or 1 4. If “investment 2 and 3 are chosen” is equivalent with (x 2 + x 3 = 2) Then “investment 4 must be chosen” is equivalent with (x 4 = 1) Based on slide (57) of the lecture, if-then statement is the following ¡ if f(x)>0 , then g(x) ≥ . ¡ Solution: we add a binary variable y, and the constraints The statement (x 2 + x 3 = 2) is equivalent to x 2 + x 3-1>0 The statement (x 4 = 1) is equivalent to x 4- 1 ≥ 0. Thus f(x)= x 2 + x 3-1 g(x)= x 4- 1 and we should add the constraints x 2 + x 3- 1 ≤ M(1 - y) 1 - x 4 ≤ My y = 0 or 1 M should be a big number such as M=20 5a. Here are four possible solutions for this question: Solution-1) You can consider if-then case: This is equivalent to: if x 2 >0 then x 1 ≥ 1000. Thus f(x)= x 2 1 ) ( ) 1 ( ) ( or y My x g y M x f = ≤ − − ≤ 2 g(x)= x 1-1000 and we should add the constraints x 2 ≤ M(1 - y) 1000 - x 1 ≤...
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This note was uploaded on 01/02/2010 for the course EMSE 202 taught by Professor Mohaghegh,abeledo during the Spring '07 term at GWU.

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HW_Solution_Chapter 09_EMSE102-202 - 1 CHAPTER 9 OR...

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