Single-Period Inventory Model - Uniform Distribution

The Kiosk sells spicy black bean burritos during the weekday lunch hour. The Kiosk charges $6.00 for each burrito and all burritos are made before the lunch crowd arrives. The burritos cost the Kiosk $1.25 each. Kiosk management is very sensitive about the quality of food they serve. Thus, they maintain a strict "No Old Burrito" policy. Thus, any burrito left at the end of the day is disposed of. Based on Kiosk's long operation history, daily demand is uniformly distributed from 56 to 87 burritos. You would need to show equations, steps, and the final results with units for full credits. Answers are in rounded-up numbers of burritos. For simplicity, all taxes and other costs are not considered.

(a) To maximize expected profit, how many burritos should Kiosk make every day?

(b) Draw a sketch of the uniform demand distribution to illustrate the business situation in part (a). Make sure to have the relevant information on the sketch.

(c) To achieve roughly 90% service level, how many burritos should Kiosk make every day?

(d) Draw another sketch of the uniform demand distribution to illustrate part (c).