As a newspaper distributor in Chicago, you are attempting to minimize oversupply

Question

As a newspaper distributor in Chicago, you are attempting to minimize oversupply to maximize profits. When you purchase the newspapers from the printer, you buy the day’s paper for $0.25 a copy. You sell a copy of the paper for $1.00. Daily demand is distributed normally with mean = 250 and standard deviation = 50. At the end of each morning, any leftover copies are worthless and they go to a recycle bin.

a. How many copies of the newspaper should you buy each morning? (Use Excel's NORMSINV() function to find the Z-score. Round intermediate calculations to four decimal places. Round your answer to the nearest whole number.)

b. Based on part (a) above, what is the probability that you will run out of stock? (Round your answer to the nearest whole percent.)

Explanation / Answer

a. Cost of underestimating the demand = $1 - $0.25 = $0.75
Cost of overestimating the demand = $0.25
Optimal probability = Cost of underestimating / ( Cost of overestimating - Cost of underestimating)
= 0.75/ (0.25 - 0.75) = 0.75

Applying NORMSINV function on 0.75, value of Z = 0.674

No. of copies of newspaper that should be bought each morning = Daily demand of newspaper ie, mean + (Probability that newspaper are not sold * Standard Deviation) = 250 + 0.674 *50 = 283.7 = 284

b. The optimal probability from above is 75%, so there is 100 - 75 = 25% probability of newspaper running out

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