The following linear programming problem has been solved by The Management Scientist. Use the

output to answer the questions.

LINEAR PROGRAMMING PROBLEM

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 Cost

X1 140.000 0.000

X2 0.000 10.000

X3 80.000 0.000

Constraint Slack/Surplus Dual Price

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. Give the complete optimal solution.

b. Which constraints are binding?

c. What is the dual price for the second constraint? What interpretation does this have?

d. Over what range can the objective function coefficient of X2 vary before a new solution

point becomes optimal?

e. By how much can the amount of resource 2 decrease before the dual price will change?

f. What would happen if the first constraint's right-hand side increased by 700 and the

second's decreased by 350?

I don't know how to do (f.)