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each store purchases the coats for $60 each; the coats are sold for $120. whatev

ID: 463599 • Letter: E

Question

each store purchases the coats for $60 each; the coats are sold for $120. whatever doesnt sell by the end of winter is put on clearance for $40.

a) what is the optimal order amount for each store?
b) what is the expected profit for the coat from each store?

after some time we decide to close our stores, sell our goods online and consolidate our inventory into a single warehouse. because of the following our clothes have, we do not expect to lose any sales as a result of the move.

c) what is the optimal order amount for the combined warehouse?
d) what is the expected profit from our coat from the combined warehouse?

Location Mean Standard Deviation 330 170 210 180 200 150 160 90

Explanation / Answer

Newspaper boy Model = C2/(C1+C2)

Where C2 is the cost of Unsold = $120-$40 =$80 (If it is not sold, you will loose profit $60 and Discount of $20)

and C1 is the Cost of Purchasing = $60

The News paper Boy Model = C2/(C1+C2) = 80/(80+60) = 0.5714

The value of Z in standrard Normal distribution when Probability= 0.5714 i 0.79

Z= 0.79

Z= (X-Mean)/SD

0.79 = (X-Mean)/SD

Calculating optimal stock for Location A , where AM=330, SD=170

0.79 =(X-330)/170

134.3=X-330

X= 464.3 , The optimal stock for Location A = 464 UNITS

Expected profit = 464*$60= $27840

The optimal stock for Location B where Average=210 and SD=180

Z= (X-MEAN)/SD

0.79= (X-210)/180

142.2= X-210

X=352.2

The optimal stock for Location B is 352 units

The expected profit = 352*$60 = $21120

The optimal stock for Location C, Where Average = 200 and SD=150

Z=(X-MEAN)/SD

0.79 = (X-200)/150

118.5= X-200

X=318.5

The optimal stock for location C = 318.5 Units

The expected profit = 318.5*$60=$19110

The optimal stock for location D, Where Average =160 and SD=90

Z=(X-MEAN)/SD

0.79 =(X-160)/90

71.1=X-160

X=231.1

The optimal stock for location D is 231.1 units

The Expected profit = 231.1*$60 = $13866

IF WE STARTED ONLINE MERCHANDISE UNDER ONE WARE HOUSE, Then our Average =900 but standrard deviation = 590 (Actually This is wrong, But no other required values given)

Optimum stock

Z=(X-MEAN)/SD

0.79 =(X-900)/590

466.1=X-900

X=466.1+900 =1366.1units

The expected profit = 1366*$60 =$81960