The Excel 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 everyone 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.

1. Write the LP for this problem using information in the Excel input sheet.

2. Use output to answer the folloewing 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?

Excel Input information

	Product unit						Decision Variables:	Units Produced
Operation	Women's Umbrelas	Golf	Men's	Folding	Units Available		Women's (W)	12
Store space in units	2	3	3	1	120		Golf (G)	0
Special display racks	1.5	2	0	0	54		Men's (M)	12
Demand	0	2	1	1	72		Follding (F)	60
Marketing	0	1	1		12
Profit	4	6	5	3.5
							Maximize Total Profit (Z) =
2. Model:
							Contraints	Hours used	<=, >=, =	Units Available
							Store space in units	120	<=	120
							Special display racks	18	<=	54
							Demand	72	<=	72
							Marketing	12	>=	12

Excel Output

Microsoft Excel 16.46 Sensitivity Report
Worksheet: [ex2.xlsx]Sheet1
Report Created: 4/3/21 3:38:01 PM
Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$I$3	Women's (W) Units Produced	12	0	4	1	2.5
	$I$4	Golf (G) Units Produced	0	-0.5	6	0.5	1E+30
	$I$5	Men's (M) Units Produced	12	0	5	2.5	0.5
	$I$6	Follding (F) Units Produced	60	0	3.5	1E+30	0.5
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$I$12	Store space in units used	120	2	120	48	24
	$I$13	Special display racks used	18	0	54	1E+30	36
	$I$14	Demand used	72	1.5	72	24	48
	$I$15	Marketing used	12	-2.5	12	12	12