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

question 18

Essay

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.
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$\begin{array} { l l } \text { Max } & 2 x _ { 1 } + x _ { 2 } \\ \text { s.t. } & 4 x _ { 1 } + 1 x _ { 2 } \leq 400 \\ & 4 x _ { 1 } + 3 x _ { 2 } \leq 600 \\ & 1 x _ { 1 } + 2 x _ { 2 } \leq 300 \\ & x _ { 1 } , x _ { 2 } \geq 0 \end{array}$

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:

Oysters

Aquatic shellfish that are cultivated or harvested for food, pearls, and shell products.

Indeterminate

describes a situation or outcome that is not precisely determined, fixed, or established, often due to insufficient information or inherent variability.

Total Utility

The overall pleasure gained from utilizing a certain quantity of goods or services.

Marginal Utility

The change in satisfaction or utility obtained by consuming an additional unit of a good or service.