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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Definitions:

Learning-Curve Coefficients

Factors that quantify the rate of improvement or learning in an operation, typically showing how costs decrease as experience increases.

Labour-Intensive

Describes industries or processes that require a large amount of manual labor input compared to capital investment.

Learning Rate

The speed at which a person or an organization improves performance or acquires knowledge over time, often resulting in reduced costs or increased proficiency.

Learning Curves

A graphical representation that shows the improvement in an individual's or organization's performance or efficiency over time due to learning and experience.