SinglePeriod Inventory Model Uniform Distribution

Yummy Burritos (YB) sells gourmet burritos during the weekday lunch hour. Yummy Burritos charges $8.00 for each burrito and all burritos are made before the lunch crowd arrives. The burritos cost YB $2.50 each. YB management maintains a strict No Old Burrito policy. Thus, any burrito left at the end of the day is discarded. Based on YBs operation history over many years, daily demand is uniformly distributed from 61 to 92 burritos.

You would need to show equations, steps, final results with units, and sketches for full credits. Quantity results are in roundedup numbers of burritos. For simplicity, all taxes and other costs are not considered.

(a)[3] To maximize expected profit, how many burritos should YB make every day? Calculate the corresponding effective service level (percentage with 1 decimal, e.g. 23.4%).

(b)[2] 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)[3] To achieve roughly 80% service level, how many burritos should YB make every day? Calculate the corresponding effective service level (percentage with 1 decimal, e.g. 23.4%).

(d)[2] Draw another sketch of the uniform demand distribution to illustrate part (c).