AQ2. (18 marks) A swimming school receives a variable number of customers for taking one-to-one private lesson everyday, and needs to schedule the number of coaches in advance. The school pays $100 for each coach scheduled to work on a specific day, regardless of whether the coach actually teaches a lesson or not. The school also charges each customer $210 for a lesson taught. There is a unit cost of $5 for processing a customer's request, no matter the customer is assigned a coach or not. If a customer cannot get a coach, the loss of customer's goodwill is regarded as $20. It has been estimated that the daily demand for the swimming lesson is normally distributed with a mean of 80 coaches and a standard deviation of 9 coaches. Given the above information, answer the following questions: 1. [4 marks] What inventory model should be used to determine the number of coaches to schedule in order to maximize the total expected profit for the school? Why? 2. (14 marks) How many coaches should be scheduled each time so as to maximize the total expected profit? (Note: Your answer should be an integer.)