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. ​ ​

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Definitions:

Conquest

The act of obtaining control over a territory or people by military force or via subjugation.

Religious Turmoil

Periods or situations marked by widespread conflict, uncertainty, or upheaval related to religious beliefs, institutions, or conflicts between different religious groups.

Colonization

The process by which a central system of power dominates the surrounding land and its components, often leading to the exploitation and oppression of indigenous peoples.

Joint-Stock Companies

These are businesses owned by shareholders who invest money in the company in exchange for a share of the profits and losses.