The LP problem whose output follows determines how many necklaces, bracelets, rings, and earrings a jewellery store should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions.

MAX

100X1+120X2+150X3+125X4

S.T.

1) X1+2X2+2X3+2X4 <108

2) 3X1+5X2+X4 <120

3) X1+X3 <25

4) X2+X3+X4>50

OPTIMAL SOLUTION

Objective Function Value = 7475.000

Variable Value Reduced Cost

X1 8.000 0.000

X2 0.000 5.000

X3 17.000 0.000

X4 33.000 0.000

Constraint Slack/Surplus Dual Price

1 0.000 75.000

2 63.000 0.000

3 0.000 25.000

4 0.000 −25.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

X1 87.500 100.000 No Upper Limit

X2 No Lower Limit 120.000 125.000

X3 125.000 150.000 162.500

X4 120.000 125.000 150.000

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

1 100.000 108.000 123.750

2 57.000 120.000 No Upper Limit

3 8.000 25.000 58.000

4 41.500 50.000 54.000

Use the output to answer the questions.

a. How many necklaces should be stocked?

b. Now many bracelets should be stocked?

c. How many rings should be stocked?

d. How many earrings should be stocked?

e. How much space will be left unused?

f. How much time will be used?

g. By how much will the second marketing restriction be exceeded?

h. What is the profit?

i. To what value can the profit on necklaces drop before the solution would change?

j. By how much can the profit on rings increase before the solution would change?

k. By how much can the amount of space decrease before there is a change in the profit?

l. You are offered the chance to obtain more space. The offer is for 15 units and the total

price is 1500. What should you do?