You are working for a large ship that operates weekly ocean cruises in the Mediterranean sea.

You are in charge of ordering the high-end specialty desserts that are offered during the cruise. Therefore, each week you must determine how many desserts (mainly cakes and pies) will go into the ship. Each cruise lasts one week, and the ship cannot be restocked during that period. The desserts are very fresh and have a short shelf life. In order to maintain your brand reputation, all non-consumed cakes must be destroyed at the end of the cruise.

Your predecessor has told you that the weekly demand for desserts is Normally distributed with a mean of 782 and a standard deviation of 145 units per week. Each dessert costs $7.50, and it is sold on the ship for $25 - they are so special that they are not free like most food on the ship.

How many desserts,, should you order to maximize the expected profit per week?

Round your answer to the nearest integer.

Part 2

What is the expected weekly profit associated to the sale of high-end specialty desserts?

Round your answer to the nearest integer.

Part 3

The SVP of Customer Care has mandated that all specialty items, such as your desserts, need to maintain a 99% cycle service level (CSL). That is, the probability of stocking out should be 1% or less. Conversely, the probability of having enough of the desserts needs to be at least 99%.

How many desserts,, should you order weekly to meet this service objective?