Solved

The Goal Programming Problem Below Was Solved with the Management

Question 2

Essay

The goal programming problem below was solved with the Management Scientist.
Min
P1(d1−) + P2(d2+) + P3(d3−)
s.t.
72x1 + 38x2 + 23x3 ≤ 20,000
.72x1 − .76x2 − .23x3 + d1− − d1+ = 0
x3 + d2− − d2+ = 150
38x2 + d3− − d3+ = 2000
x1, x2, x3, d1−, d 1+, d2−, d2+, d3−, d3+ ≥ 0
Partial output from three successive linear programming problems is given. For each problem, give the original objective function expression and its value, and list any constraints needed beyond those that were in the original problem. The goal programming problem below was solved with the Management Scientist. Min P<sub>1</sub>(d<sub>1</sub>−) + P<sub>2</sub>(d<sub>2</sub><sup>+</sup>) + P<sub>3</sub>(d<sub>3</sub>−) s.t. 72x<sub>1</sub> + 38x<sub>2</sub> + 23x<sub>3</sub> ≤ 20,000 .72x<sub>1</sub> − .76x<sub>2</sub> − .23x<sub>3</sub> + d<sub>1</sub>− − d<sub>1</sub><sup>+</sup> = 0 x<sub>3</sub> + d<sub>2</sub>− − d<sub>2</sub><sup>+</sup> = 150 38x<sub>2</sub> + d<sub>3</sub>− − d<sub>3</sub><sup>+</sup> = 2000 x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub>, d<sub>1</sub>−, d <sub>1</sub><sup>+</sup>, d<sub>2</sub>−, d<sub>2</sub><sup>+</sup>, d<sub>3</sub>−, d<sub>3</sub><sup>+</sup> ≥ 0 Partial output from three successive linear programming problems is given. For each problem, give the original objective function expression and its value, and list any constraints needed beyond those that were in the original problem. ​ ​ ​ The goal programming problem below was solved with the Management Scientist. Min P<sub>1</sub>(d<sub>1</sub>−) + P<sub>2</sub>(d<sub>2</sub><sup>+</sup>) + P<sub>3</sub>(d<sub>3</sub>−) s.t. 72x<sub>1</sub> + 38x<sub>2</sub> + 23x<sub>3</sub> ≤ 20,000 .72x<sub>1</sub> − .76x<sub>2</sub> − .23x<sub>3</sub> + d<sub>1</sub>− − d<sub>1</sub><sup>+</sup> = 0 x<sub>3</sub> + d<sub>2</sub>− − d<sub>2</sub><sup>+</sup> = 150 38x<sub>2</sub> + d<sub>3</sub>− − d<sub>3</sub><sup>+</sup> = 2000 x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub>, d<sub>1</sub>−, d <sub>1</sub><sup>+</sup>, d<sub>2</sub>−, d<sub>2</sub><sup>+</sup>, d<sub>3</sub>−, d<sub>3</sub><sup>+</sup> ≥ 0 Partial output from three successive linear programming problems is given. For each problem, give the original objective function expression and its value, and list any constraints needed beyond those that were in the original problem. ​ ​ ​ The goal programming problem below was solved with the Management Scientist. Min P<sub>1</sub>(d<sub>1</sub>−) + P<sub>2</sub>(d<sub>2</sub><sup>+</sup>) + P<sub>3</sub>(d<sub>3</sub>−) s.t. 72x<sub>1</sub> + 38x<sub>2</sub> + 23x<sub>3</sub> ≤ 20,000 .72x<sub>1</sub> − .76x<sub>2</sub> − .23x<sub>3</sub> + d<sub>1</sub>− − d<sub>1</sub><sup>+</sup> = 0 x<sub>3</sub> + d<sub>2</sub>− − d<sub>2</sub><sup>+</sup> = 150 38x<sub>2</sub> + d<sub>3</sub>− − d<sub>3</sub><sup>+</sup> = 2000 x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub>, d<sub>1</sub>−, d <sub>1</sub><sup>+</sup>, d<sub>2</sub>−, d<sub>2</sub><sup>+</sup>, d<sub>3</sub>−, d<sub>3</sub><sup>+</sup> ≥ 0 Partial output from three successive linear programming problems is given. For each problem, give the original objective function expression and its value, and list any constraints needed beyond those that were in the original problem. ​ ​

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