You are a newsvendor selling San Pedro Times every morning. Before you get to wo
ID: 435856 • Letter: Y
Question
You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day's paper for $0.30 a copy. You sell a copy of San Pedro Times for $1.50. Daily demand is distributed normally with mean 285 and standard deviation 57. At the end of each morning, any leftover copies are worthless and they go to a recycle bin. a. How many copies of San Pedro Times should you buy each morning? (Use Excel's NORMSINV() function to find the correct critical value for the given ?- level. Round your z-value to 2 decimal places and final answer to the nearest whole number.) Optimal order quantity b. Based on a, what is the probability that you will run out of stock? (Round your answer to the nearest whole number.) ProbablityExplanation / Answer
Ans a)
The selling price of newspaper = $1.50
Cost price of newspaper = $0.30
The cost of underage (Cu) = Selling price - Cost price
= 1.50 - 0.30
= $1.20
The cost of overage (Co) = Cost price of newspaper
= $0.30
Optimal probability = Cost of underage / (Cost of underage + Cost of overage)
= 1.20 / (1.20 + 0.30)
= 1.2 / 1.5
= 0.8
Using the NORMSINV function in Excel, for an optimal probability of 0.8, the Z- value is given by 0.84.
The optimal order quantity = Mean demand + Z-value * Standard deviation of demand
= 285 + 0.84 * 57
= 333 copies
Ans b)
The optimal probability was equal to 80% in part a. Thus, there is a 20% probability that the newsvendor will run out of stock if he purchases 333 copies of San Pedro Times.
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