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:

Glycerine

A simple polyol compound used in foods, pharmaceuticals, and cosmetics for its moisturizing and solvent properties.

Nitric Acid

A highly corrosive and strong mineral acid with the formula HNO3, commonly used in the production of fertilizers, explosives, and in various nitration processes.

Williamson Ether Synthesis

An organic reaction forming an ether from an organohalide and an alcohol in the presence of a strong base.

Efficient Use

A method or strategy that aims to achieve maximum productivity with minimum wasted effort or expense.