Problem
Pizza USA, Inc., produces and markets pizzas on a national basis. The shop manager decides how many pizzas to be made. He learns that daily demand for pizza follows a normal distribution of mean 300 and standard deviation 50.
I. The manager estimates that he will be able to make profit if he sells more than 350 pizzas. The manager expects to get incentive only if he makes profit. What is the probability that the manager receives incentive?
II. The manager is also aware that if the sale drops below 150, then he receives a pay cut. What is the probability that he receives a pay cut?
III. What is the probability that the pizza sales is within 10% of the average value?
IV. If the manager has materials to make only 200 pizzas for a given day with the raw materials available with him, how much is the expected lost sales assuming there is no way that additional raw materials can be purchased for that day?
V. If the manager wants the expected lost sales to be 50 pizzas or lower, then how much raw materials (equivalent to how many pizzas) must he store at the beginning of the day?