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?