Consider the following linear program: MAX 3x₁ + 4x₂ ($ Profit) s.t.x₁ + 3x₂

Question

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

Consider the following linear program: MAX 3x<sub>1</sub> + 4x<sub>2</sub> ($ Profit) s.t.x<sub>1</sub> + 3x<sub>2</sub> < 12 2x<sub>1</sub> + x<sub>2</sub> < 8 x<sub>1</sub> < 3 x<sub>1</sub>,x<sub>2 </sub> > 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 x<sub>1</sub> 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 x<sub>2</sub> was $10 instead of $4,would the optimal solution change? d.If simultaneously the profit on x<sub>1</sub> was raised to $5.5 and the profit on x<sub>2</sub> was reduced to $3,would the current solution still remain optimal?

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?

Quizplus · Accepted Answer

The Answer of 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?

Consider the Following Linear Program