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 x1 increased 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?