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

question 28

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 $\le$ 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.

Apply special product patterns to simplify polynomial expressions.

Multiply and simplify polynomial expressions using vertical format.

Determine the area or volume of geometric figures using polynomial expressions.

Simplify expressions involving powers and exponents.

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Definitions:

Utility Maximizing

Acting in a way to achieve the highest level of satisfaction possible with available resources.

Demand For Labor

The total amount of labor that employers want to hire at various wage rates, contingent on factors such as technology, the price of the goods being produced, and the availability of other inputs.

Reduced Wage

A wage that is decreased from a previous level, often due to economic pressures or changes in job responsibilities.

Income Effect

The alteration in a person's or economic system's earnings and the effect of this alteration on the demand for a particular product or service.