8. Lab Week 9 Problem Solutions

8. Lab Week 9 Problem Solutions - as the acceptable region....

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Lab Week 9 Problem Solutions CHAPTER 9 GOAL PROGRAMMING 1. Minimize P 1 u 1 , P 2 u 2 , P 3 u 3 . (P 1 u 1 represents underutilization of labour, P 2 u 2 represents underutilization of profit, and P 3 u 3 represents underutilization of product 1) Add the underutilization (u i ) and overutilization (v i ) variables to each constraint as well as the profit. Storage is the only non-goal since it is not subject to any minimization or maximizations. Minimize P 1 u 1 +P 2 u 2 + P 3 u 3 . Subject to Labour: 2x 1 +x 2 +4x 3 +u 1 -v 1 =160 hours Profit: 4x 1 +2x 2 +3x 3 +u 2 -v 2 =300 (dollars) Product 1: x 1 +u 3 -v 3 =10 units Storage: x 1 +2x 2 +3x 3 ≤150 square feet All variables ≥ 0 3. a. Soft because of the deviation variables present. b. Minimizing the underutilization of the second constraint. c. First graph the second constraint since it is the first priority. (x 1 =80) Since we are minimizing underutilization, we will consider the line and everything to the right
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Unformatted text preview: as the acceptable region. Then graph the first constraint. (x 2 =60-x1) Since we are minimizing overutilization, we consider the area to the left as the acceptable region. Since the two regions do not overlap, we choose a point in the first region that is closest to the second: x 1 =80, x 2 =0. Thus, u 2 =0,v 1 =200. d. Even though this changes the priorities, the acceptable regions would still be the same; however we would choose a point from constraint ones region that is closest to the other acceptable region: x 1 =60, x 2 =0. Thus, v 1 =0, u 2 =20. 9. Note: Profit is a hard constraint. S=1.1, T=7.02, v 1 =0, u 2 =0, u 3 =2.98, u 4 =7.90 13....
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8. Lab Week 9 Problem Solutions - as the acceptable region....

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