Solutions Optimization

Solution) The following output represent a problem whose solution will tell a specialty retailer how many of f

Question: The following 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.

Use the output on the next page 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?

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