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?
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
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