(a) Write an expression for the expected sales of Model Z at BPT for a given stock level choice Q, i.e., the expected number of Model Z's that BPT will sell in the next three months . (This expression should be detailed enough that if we knew BPT's stock level choice (Q). the fraction of total demand that BPT gets (k), the functions F and f, and had a tool at our disposal to evaluate integrals, then we could evaluate this expression.) (b) Using your answer to part (a), write an expression for the expected prot BPT will make from Model Z. (c) Using your answer to part (b), derive a relationship that needs to be satisfied by BPT's optimal stock level. Problem 3- A retailer is going to start selling Sharp6 ,the latest razor to be released by Sharp, which has six blades. The retailer is going to review the inventory level of Sharp6 at the beginning of each week , at which point they will place a new order to bring the inventory level of Sharp6 to an order-up-to level, denoted by Q. Assume that the leadtime is negligible , so that the retailer receives the razors immediately after placing the order . The weekly demand for Sharp6 is normally distributed with a mean of 150 units and a variance of 225. The demands in any two weeks are independent from each other. The retailer buys Sharp6 at $5 per unit , and sells it at $10 per unit . The retailer has limited space , and could have used the shelfspace occupied by Sharp6 to store some other products .Therefore ,there is an opportunity cost of carrying Sharp6 in inventory. The opportunity cost is $1 per unit per week . Given this information , answer the following questions independently from one another (a) If a customer nds that the retailer has run out of Sharp6 ,there is a 50% chance that the customer will buy Sharp4 , the older version of razors from Sharp , which has 4 blades . Customers who do not switch to Sharp4 will be lost to a competitor .The retailer buys Sharp4 at $4 per unit and sells it at $7 per unit . Given this information , what order up to level , Q, should the retailer use for Sharp6 in order to minimize the expected underage and overage costs? (b) If a customer nds that the retailer has run out of Sharp6 ,then the customer will be lost to a competitor . By a study of consumer data , the retailer knows that 50% of customers who buy razors also buy shaving foam . The shaving foam costs the retailer $5 per unit and its retail price is $8. The retailer assumes that, if a customer who was planning on buying both the razor and the shaving foam nds that the razor is out of stock , then the customer will not buy the shaving foam either .Given this information ,what order up to level, Q, should the retailer use for Sharp6 in order to minimize the expected underage and overage costs? (c) Suppose that the retailer chooses an order up-to level of 120. With this choice for the order-up-to level, in any given week, what is the probability that the retailer will run out of Sharp6