Scenario 13.1 - Nefarious
The tenured professor routinely led student groups on factory tours in exotic locales,and one popular destination was an island south of Miami.The students enjoyed this happy little island and the professor liked it because he could supplement his income by bringing back a few boxes souvenirs he could sell to his friends.The souvenirs cost the professor $125 a box and he sells them for $290 a box.Souvenirs that dry out due to age can be sold for $80.Experience has shown that the demand for boxes of these souvenirs has a mean of 80 with a standard deviation of 20.
-Naturally,the professor will purchase the optimal number of boxes.(He's had a course or two in supply chain management and knows this model well. )If each of his friends purchases only one box,how many friends will he turn away because he runs out of boxes of souvenirs?
A)5
B)3
C)2
D)1

Question

Quizplus · Accepted Answer

To determine the optimal number of boxes to purchase, the professor needs to calculate the expected demand for souvenirs. The mean demand is 80 boxes with a standard deviation of 20. Using a z-score table or calculator, we can determine that the z-score corresponding to a demand of 80 is 0. If the professor wants to ensure that he has enough souvenirs to meet demand, he should order enough boxes to cover one standard deviation above the mean, which would be 100 boxes.

The cost of 100 boxes of souvenirs would be $12,500 ($125 per box), and he could sell them for $29,000 ($290 per box). If the professor sells all 100 boxes, he would make a profit of $16,500. However, not all boxes may sell at full price. Based on experience, we know that some may dry out and can only be sold for $80. Let's assume that 10% of the boxes can only be sold for $80. This means that 90% of the boxes can be sold for the full price of $290, and 10% can be sold for $80.

Expected profit = (0.9)(100)(290-125) + (0.1)(100)(80-125)
Expected profit = $15,500

Therefore, the professor should purchase 100 boxes of souvenirs. If each of his friends purchases only one box, he will sell 90% of the boxes for the full price of $290, which would sell out 90/290 = 31 friends. The remaining 10% could be sold for $80, which would sell out 10/80 = 1.25 friends. Since he can't sell a partial box, he will have to turn away 2 friends (31+1=32, but he only has 30 boxes at the $80 price). Therefore, the answer is C) 2.