Scenario 16.4 - Santorini Donkeys
Sturdy little donkeys are used to carry corpulent tourists up the Santorini caldera to the town of Fira.One cruise line that routinely docks at the port is considering a plan to maintain their own donkey herd,which will cost them $15,000 per thousand tourists.The number of tourists needing this service is normally distributed,with a mean of 10,000 and a standard deviation of 3,000.Usually,this is enough donkey capacity,but occasionally the cruise line rotates a bigger ship through this route and the excursion director must purchase donkey capacity on the spot market,where is costs $20 per tourist.
-The cruise line's insurance policy limits the number of donkeys in their herd to 5,000.What bulk price should the cruise line negotiate to make the 5,000 donkey herd size optimal?
A)$16,664 per ten thousand
B)$16,362 per ten thousand
C)$16,134 per ten thousand
D)$15,978 per ten thousand

Question

Quizplus · Accepted Answer

The optimal bulk price is the price at which the expected cost of maintaining the donkey herd is equal to the expected cost of purchasing donkey capacity on the spot market. The expected cost of maintaining the donkey herd is $15,000 per thousand tourists, so the expected cost of maintaining a herd of 5,000 donkeys is $15,000 * 5 = $75,000. The expected cost of purchasing donkey capacity on the spot market is $20 per tourist, so the expected cost of purchasing donkey capacity for 10,000 tourists is $20 * 10,000 = $200,000. The optimal bulk price is the price at which the expected cost of maintaining the donkey herd is equal to the expected cost of purchasing donkey capacity on the spot market, so the optimal bulk price is $75,000 / 10,000 = $16,664 per ten thousand.