Homework SourseUse the following Management Scientist output to answer the
Use the following Management Scientist output to answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX 31X1+35X2+32X3
S.T.
1) 3X1+5X2+2X3>90
2) 6X1+7X2+8X3<150
3) 5X1+3X2+3X3<120
OPTIMAL SOLUTION
Objective Function Value = 763.333
Variable
Value
Reduced Cost
X1
13.333
0.000
X2
10.000
0.000
X3
0.000
10.889
Constraint
Slack/Surplus
Dual Price
1
0.000
-0.778
2
0.000
5.556
3
23.333
0.000
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
Current Value
Upper Limit
X1
30.000
31.000
No Upper Limit
X2
No Lower Limit
35.000
36.167
X3
No Lower Limit
32.000
42.889
RIGHT HAND SIDE RANGES
Constraint
Lower Limit
Current Value
Upper Limit
1
77.647
90.000
107.143
2
126.000
150.000
163.125
3
96.667
120.000
No Upper Limit
a. Give the complete optimal solution to the problem.
b. Which constraints are binding?
c. What would happen if the coefficient of x1increased by 3?
d. What would happen if the right-hand side of constraint 1 increased by 10?
E. what would happen if the coefficient if x2 increased by 2?
f. what would happen if the coefficient if x2 descreased by 2?
g. what would happen if the coefficient if x2 descreased by 5?
h. what would happen if the right hand side of constraint 3 increased by 10?
i. what would happen if the right hand side of constraint 2 increased by 10?
j. if the right-hand side of constraint 2 can be increased by 10 at a cost of $50, what is your suggestion?
k. if the company can add extra 10 hours at no cost, in which department should these hours be added?
| Variable | Value | Reduced Cost |
| X1 | 13.333 | 0.000 |
| X2 | 10.000 | 0.000 |
| X3 | 0.000 | 10.889 |
Solution
