A popular newsstand in a large metropolitan area is attempting to determine how

Question

A popular newsstand in a large metropolitan area is attempting to determine how many copies of the daily newspaper it should purchase. Daily demand can be approximated by a normal probability distribution with mue- 450 and standard deviation 100. The newspaper costs the newsstand $.45 per copy and sells for $1.00 per copy. The newsstand can return any unsold newspapers and receive a $.25 rebate. A) How many copies of the newspaper should be purchased each day? B) what is the probability that the newsstand will have a stock out?

Explanation / Answer

Demand = 450

Std Dev = 100

Underage Cost = Selling Price - Cost Price = 1 - 0.45 = 0.55

Overage Cost = Cost Price - Salvage Value = 0.45 - 0.25 = 0.20

Critical Ratio = Underage Cost / (Underage Cost + Overage Cost) = 0.55/ (0.55+0.20) = 0.7333

From Z table, Z value for 0.7333 = 0.625

Quantity to be purchased for max profit = Demand + Z * Std Dev = 450 + 0.625*100 = 512.5 ~ 512 newspapers

Stock Out Probability = 1 - Critical ratio = 0.2666 = 26.66%

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