# Linear equation: Q2

#### San1998

##### New member
Q2
The following linear programming problem has been solved by The Management Scientist. Use the
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.)