Q4:
The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Use the output to answer these questions.
MAX 4X1+6X2+7X3
S.T.
1) 3X1+2X2+5X3 <120
2) 1X1+3X2+3X3 <80
3) 5X1+5X2+8X3 <160
4) +1X3 >10
OPTIMAL SOLUTION
Objective Function Value = 166.000
Variable Value Reduced Cost
X1 0.000 2.000
X2 16.000 0.000
X3 10.000 0.000
Constraint Slack/Surplus Dual Price
1 38.000 0.000
2 2.000 0.000
3 0.000 1.200
4 0.000 −2.600
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
X1 No Lower Limit 4.000 6.000
X2 4.375 6.000 No Upper Limit
X3 No Lower Limit 7.000 9.600
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 82.000 120.000 No Upper Limit
2 78.000 80.000 No Upper Limit
3 80.000 160.000 163.333
4 8.889 10.000 20.000
a. How much of ingredient 1 will be put into the blend?
b. How much of ingredient 2 will be put into the blend?
c. How much of ingredient 3 will be put into the blend?
d. How much resource A is used?
e. How much resource B will be left unused?
f. What will the profit be?
g. What will happen to the solution if the profit from ingredient 2 drops to 4?
h. What will happen to the solution if the profit from ingredient 3 increases by 1?
i. What will happen to the solution if the amount of resource C increases by 2?
j. What will happen to the solution if the minimum requirement for ingredient 3 increases to
15?
The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Use the output to answer these questions.
MAX 4X1+6X2+7X3
S.T.
1) 3X1+2X2+5X3 <120
2) 1X1+3X2+3X3 <80
3) 5X1+5X2+8X3 <160
4) +1X3 >10
OPTIMAL SOLUTION
Objective Function Value = 166.000
Variable Value Reduced Cost
X1 0.000 2.000
X2 16.000 0.000
X3 10.000 0.000
Constraint Slack/Surplus Dual Price
1 38.000 0.000
2 2.000 0.000
3 0.000 1.200
4 0.000 −2.600
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
X1 No Lower Limit 4.000 6.000
X2 4.375 6.000 No Upper Limit
X3 No Lower Limit 7.000 9.600
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 82.000 120.000 No Upper Limit
2 78.000 80.000 No Upper Limit
3 80.000 160.000 163.333
4 8.889 10.000 20.000
a. How much of ingredient 1 will be put into the blend?
b. How much of ingredient 2 will be put into the blend?
c. How much of ingredient 3 will be put into the blend?
d. How much resource A is used?
e. How much resource B will be left unused?
f. What will the profit be?
g. What will happen to the solution if the profit from ingredient 2 drops to 4?
h. What will happen to the solution if the profit from ingredient 3 increases by 1?
i. What will happen to the solution if the amount of resource C increases by 2?
j. What will happen to the solution if the minimum requirement for ingredient 3 increases to
15?