The optimal value of the objective function

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Reference no: EM132299320

Consider the following linear program:

MAX 3x1 + 4x2 ($ Profit)

s.t. x1 + 3x2 < 12

2x1 + x 2 < 8

x1 < 3

x1, x2 > 0

The Management Scientist provided the following solution output:

OPTIMAL SOLUTION

Objective Function Value = 20.000

Variable Value Reduced Cost

X1 2.400 0.000

X2 3.200 0.000

Constraint Slack/Surplus Dual Price

1 0.000 1.000

2 0.000 1.000

3 0.600 0.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

X1 1.333 3.000 8.000

X2 1.500 4.000 9.000

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

1 9.000 12.000 24.000

2 4.000 8.000 9.000

3 2.400 3.000 No Upper Limit

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?

Reference no: EM132299320

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