i have posted my answer below but I am not sure I am right 1. (Newsboy model) Ne
ID: 446574 • Letter: I
Question
i have posted my answer below but I am not sure I am right
1. (Newsboy model) Needless Markup (NM), a famous “high end” department store, must decide on the quantity of a high-priced woman’s handbag to procure in Spain for the coming Christmas season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150.00. Any handbags not sold by the end of the season are purchased by a liquidator for $10.00 each. In addition, the store accountants estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this dollar invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold bags only.
a) Due to the long distance and limited capacity, NM must place the order 6 months in advance. A detailed analysis of past data shows that if forecasting 6 month in advance, the number of bags sold can be described by a normal distribution, with mean 150 and standard deviation 60. What is the optimal number of bags to purchase?
b) What is the expected cost of mis-match under the optimal purchase quantity?What is the optimal expected profit
A.) Optimal number of bags to purchase is 216.98 or 217 B.) The expected cost of mismatch is 1797.16 The expected profit is 16427.84Explanation / Answer
The newspaper boy Model Problem C1/ (C1+C2),
Where C1 is the cost of unsold and c2 is the profit
The cost of unsold C1= $150-$28.5-$10+$0.4 =$111.9
( If Unsold , you are losing a profit of ($150-$28.5), an income of $10, an expense of $0.40 at the inventory)
The Profit C2= = $150-$28.5 = $121.5
The paper boy model = C1/ (C1+C2) = $111.9/(111.9+121.5) = 0.4794
In the above problem It is given given that Mean is 150 and Standard Deviation is 60
Now The Quantity Required is
Z= (X-Mean)/SD
It is given that the probability is 0.4794, The table value of Z in Standard normal distribution when probability = 0.4794 is 2.04
I.e
Z= (X-Mean)/SD
2.04 = (X-150)/60
2.04*60 = x-150
X= 272.4
The number of Qunatities to be purchased = 272.4
The remaining calculation as you calculated ealry but should be based on the new figure.
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