# Range of optimality

The following linear programming problem has been solved by The Management Scientist. Use the output below to determine the range of optimality for variable X3.

MAX 25X1+30X2+15X3

S.T.

1) 4X1+5X2+8X3<1200

2) 9X1+15X2+3X3<1500

OPTIMAL SOLUTION

Objective Function Value = 4700.000

Variable Value Reduced Costs

X1 140.00 0.00

X2 0.000 10.00

X3 80.00 0.00

Constraint Slack/Surplus Dual Prices

1 0.000 1.000

2 0.000 2.333

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

X1 19.286 25.000 45.000

X2 No Lower Limit 30.000 40.000

X3 8.333 15.000 50.000

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

1 666.667 1200.000 4000.000

2 450.000 1500.000 2700.000

a (25,45)

b (450,2700)

c (15,50)

d (8.33, 50)

e (19.29,45)

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#### Solution Preview

Correct, we can find the range for X3 by using the "OBJECTIVE COEFFICIENT RANGES"

Variable ...

#### Solution Summary

The solution answers the question below.