'The Happy Smiles' is a start-up that makes healthy meals available to home-quarantined COVID-19 patients in India. Every morning a cook prepares a certain amount of food that is packed in meal boxes. Then they deliver the meal boxes to those who order via an app. Meal boxes can only be prepared in the early morning (they cannot be replenished throughout the day) and meal boxes that are not sold must be discarded at the end of the day. Meghana is an intern who has joined this start-up for the summer.

Having gained her skills in SC1x recently, she decides to run some statistics to help the company plan better. She notices that the daily demand for meal boxes follows a normal distribution with a mean of 1533 and a standard deviation of 53. The selling price of a meal box is 136 INR (Indian Rupee) and it costs 30 INR to prepare it.

Question 1:

Based on the data provided, how many meal boxes should the company prepare every morning to maximize their daily profit?

Question 2:

What is the cycle service level that the company would be providing if they prepared the number of meal boxes calculated in Question 1?

Question 3:

What is the estimated number of meal boxes they would fall short every day if they prepared the number of meal boxes calculated in Question 1?

Question 4:

What is the expected daily profit perceived by the company if they prepared the number of meal boxes calculated in Question 1?