4. The LP model and output below 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 (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing that you need to solve for this problem. All questions below can be answered by the output. MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4 SUBJECT TO

	1) 2 X1 + 3 X2 + 3 X3 + X4
	2) 1.5 X1 + 2 X2
	3) 2 X2 + X3 + X4
	4) X2 + X3 >= 12 Answer Report (Note the order of the constraints. Excel placed them out of order so make sure you see that Constraint 1 is the second constraint listed and constraint 4 is the first constraint listed).

Sensitivity Report (See note above regarding order of constraints).

END Use the output to answer the questions.

a.	How many women's umbrellas (X1) should be stocked?
b.	How many golf umbrellas (X2) should be stocked?
c.	How many men's umbrellas (X3) should be stocked?
d.	How many folding umbrellas (X4) 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? Why?

402 1 Microsoft Excel 16.0 Answer Report 2 Worksheet: (Handout Transportation Excel Solutions Zrock and .xlsx]Acme (2) 3 Report Created: 3/28/2020 5:31:11 PM 4 Result: Solver found a solution. All constraints and optimality conditions are satisfied. 5 Solver Engine 6 Engine: Simplex LP 7 Solution Time: 0.078 Seconds. 8 Iterations: 7 Subproblems: 0 9 Solver Options 10 Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling 11 Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative 12 13 14 Objective Cell (Max) 15 Cell Name Original Value Final Value 16 $B$1 Profit 0 17 18 19 Variable Cells 20 Cell Name Original Value Final Value Integer 21 $B$4 Amount X1 0 12 Contin 22 $C$4 Amount x2 0 O Contin 23 $D$4 Amount X3 0 12 Contin 24 $E$4 Amount X4 0 60 Contin 25 26 27 Constraints 28 Cell Name Cell Value Formula Status Slack 29 SG$10 Constraint 4 12 $G$10>=$F$10 Binding 0 30 $G$7 Constraint 1 120 SG$7