How many womens umbrellas should be stocked

Assignment Help Operation Management

Reference no: EM131854911

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?

Reference no: EM131854911

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