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.
-Once a local donkey herder learns of the cruise line's plan,he lowers his donkey rental price to $17.50 per tourist.How many donkeys should be in the cruise line's herd?
A)7,264
B)6,684
C)6,711
D)6,797

Question

Quizplus · Accepted Answer

To determine the optimal number of donkeys, we need to calculate the point at which the expected cost of maintaining the herd plus the expected cost of additional capacity equals the cost of using the local herder's services for all tourists. This involves finding the z-score where the cost of additional capacity on the spot market equals the cost savings from owning the donkeys. Using the given mean, standard deviation, and costs, the calculation leads to the determination that maintaining a herd to cover the demand up to a certain z-score (which corresponds to the demand level) minimizes the total expected cost. The exact number of donkeys, 6,797, is derived through this calculation, taking into account the normal distribution of tourist numbers and the costs associated with each option.