Consider the Following Linear Program

question 43

Essay

Consider the following linear program:
MAX 3x₁ + 4x₂ ($ Profit)
s.t.x₁ + 3x₂ < 12
2x₁ + x₂ < 8
x₁ < 3
x₁,x₂ > 0
The Management Scientist provided the following solution output:
OPTIMAL SOLUTION
Objective Function Value = 20.000
OBJECTIVE COEFFICIENT RANGES
RIGHT HAND SIDE RANGES

a.What is the optimal solution including the optimal value of the objective function?
b.Suppose the profit on x₁ is increased to $7.Is the above solution still optimal? What is the value of the objective function when this unit profit is increased to $7?
c.If the unit profit on x₂ was $10 instead of $4,would the optimal solution change?
d.If simultaneously the profit on x₁ was raised to $5.5 and the profit on x₂ was reduced to $3,would the current solution still remain optimal?

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