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.

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?

LINEAR PROGRAMMING PROBLEM

MAX 4X1+6X2+7X3

S.T.

1) 3X1+2X2+5X3<1202) 1X1+3X2+3X3<803) 5X1+5X2+8X3<1604) +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