A cafeteria buys muffins daily. Demand varies Uniformly between 30 and 50 muffins per day. The cafeteria pays $.20 per muffin and charges $.80 per muffin. Unsold muffins are discarded at the end of the day.

A) Find the optimal stocking level and the stock-out risk for that quantity.

The optimal stocking level is 45 muffins.

Explanation:

First we have to calculate the Overage cost Co = Purchase price - Salvage value = $0.2 - 0 = $0.2

Then the Underage cost Cu = Selling price - Purchase price = $0.80 - $0.2 = $0.60

Service level = Cu / (Cu + Co) = $0.60 / ($0.60+$0.2) = $0.75

Hence, optimal stocking level = Minimum demand + Service level * (Maximum demand - Minimum demand)

optimal stocking level = 30 + 0.75 * (50-30) = 45

The optimal stocking level is 45 muffins.

Optimal stocking level = 68.75 Muffins