The Lofton Company Has Developed the Following Linear Programming Problem

question 14

Essay

The Lofton Company has developed the following linear programming problem
Max
x₁ + x₂
s.t.
2x₁ + x₂ ≤ 10
2x₁ + 3x₂ ≤ 24
3x₁ + 4x₂ ≥ 36
​
but finds it is infeasible. In revision, Lofton drops the original objective and establishes the three goals
Goal 1:
Don't exceed 10 in constraint 1.
Goal 2:
Don't fall short of 36 in constraint 3.
Goal 3:
Don't exceed 24 in constraint 2.
​
Give the goal programming model and solve it graphically.

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