The Optimal Solution of the Linear Programming Problem Is at the Intersection

question 56

Essay

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.
Max
2x₁ + x₂
s.t.
4x₁ + 1x₂ ≤ 400
4x₁ + 3x₂ ≤ 600
1x₁ + 2x₂ ≤ 300
x₁ , x₂ ≥ 0
​
a.​Over what range can the coefficient of x₁ vary before the current solution is no longer optimal?
b.​Over what range can the coefficient of x₂ vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.

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