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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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