The LP model and LINDO output represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's, golf, men's, and folding umbrellas, respectively. The constraints measure storage space in units, special display racks, demand, and a marketing restriction, respectively.

MAX 4 X1 + 6 X2 + 5 X3 + 3.5 X4

SUBJECT TO

2)2 X1 + 3 X2 + 3 X3 + X4 <= 120 3)1.5 X1 + 2 X2 <= 54 4)2 X2 + X3 + X4 <= 72 5)X2 + X3 >= 12

END

OBJECTIVE FUNCTION VALUE

1)318.00000

VARIABLE

VALUE

REDUCED COST

X1

12.000000

.000000

X2

.000000

.500000

X3

12.000000

.000000

X4

60.000000

.000000

ROW

SLACK OR SURPLUS

DUAL PRICE

2)

.000000

2.000000

3)

36.000000

.000000

4)

.000000

1.500000

5)

.000000

-2.500000

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ. COEFFICIENT RANGES

VARIABLE

CURRENT

COEFFICIENT

ALLOWABLE

INCREASE

ALLOWABLE

DECREASE

X1

4.000000

1.000000

2.500000

X2

6.000000

.500000

INFINITY

X3

5.000000

2.500000

.500000

X4

3.500000

INFINITY

.500000

RIGHTHAND SIDE RANGES

ROW

CURRENT

RHS

ALLOWABLE

INCREASE

ALLOWABLE

DECREASE

2

120.000000

48.000000

24.000000

3

54.000000

INFINITY

36.000000

4

72.000000

24.000000

48.000000

5

12.000000

12.000000

12.000000

Use the output to answer the questions.

a. How many women's umbrellas should be stocked? b. How many golf umbrellas should be stocked? c. How many men's umbrellas should be stocked? d. How many folding umbrellas should be stocked? e. How much space is left unused? f. How many racks are used? g. By how much is the marketing restriction exceeded? h. What is the total profit? i. By how much can the profit on women's umbrellas increase before the solution would change? j. To what value can the profit on golf umbrellas increase before the solution would change? k. By how much can the amount of space increase before there is a change in the dual price? l. You are offered an advertisement that should increase the demand constraint from 72 to 86 for a total cost of $20. Would you say yes or no?