What Is the Smallest Value of the Objective Function Coefficient

question 49

Essay

What is the smallest value of the objective function coefficient X₁ can assume without changing the optimal solution?
MAX: ^{7 X}₁ ^{+ 4 X}₂
Subject to: ^{2 X}₁ ^{+ X}₂ ^{≤ 16}
X₁ + X₂ ≤ 10
2 X₁ + 5 X₂ ≤ 40 X₁,X₂ ≥ 0

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