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.

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Definitions:

[H+]

[H+] denotes the concentration of hydrogen ions in a solution, which is a measure of the acidity or alkalinity (pH) of the solution.

K

The chemical symbol for Potassium, a soft, silver-white metal belonging to the alkali metal group of the periodic table.

[H+]

A notation representing the concentration of hydrogen ions in solution, often used in the context of acidity or pH levels.

K

Symbol for Potassium, a chemical element with atomic number 19, essential for various bodily functions including nerve signal transmission and muscle contraction.