this problem should be done by using the Newsvendor model. Please show explicitly how to calculate the critical ratio. i.e. cost of overage and underage).

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.)