Question

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. 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 it costs $20 per tourist.

 

I. How many donkeys should the cruise line have in its herd?

II. Once a local donkey herder learns of the cruise line's plan, he raises his donkey rental price to $25 per tourist. How many donkeys should be in the cruise line's herd?

III. 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?

IV. 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?

Answer 1

Cost to maintain own herd per donkey = 15000/1000 = 15

IV.

For 5000 herd size, z-stat = (5000-10000)/3000 = -1.667

Corresponding probability/critical ratio = NORMSDIST(-1.667) = 0.0477

Cu/(Cu+Co) = (local herder cost - cost to maintain own)/local herder cost = 0.0477

Local herder cost = $ 15.75

The cruise line should negotiate a bulk price of $ 15.75 with the local herder to make the 5000 donkey herd size optimal.