MBI is a manufacturer of personal computers. All of its personal computers use a hard drive that it purchases from a single supplier, Ynos. MBI operates its factory 52 weeks per year, which requires assembling 100 of these hard drives into computers per week. MBI's annual holding cost is quantified by a rate of return of 20% of the value of the inventory. The administrative cost of placing an order for hard drives with Ynos has been estimated to be $50 (independent of the order size). The purchase cost of one hard drive from Ynos is $100. a. What is the optimal order size of hard drives for this system? (5 points) b. What is the resulting total annual cost of this system? (4 points) c. What is the time between orders (in weeks)? (4 points) d. Now suppose that a quantity discount is offered by Ynos for large orders as shown below. What is the optimal order quantity? (8 points) Discount 1 2 3 Quantity 1 to 99 100 to 499 500 or larger Price per item 1005 95$ 90$ Now suppose that you can manufacture the product in house and will no longer get your and holding rates remain unchanged, answer the following questions (parts e and f): to run the production machine, i.e., each production run requires a $500 set-up cost. If the demand Ynos. You can manufacture an item at a price of $70 and at a rate of 600 items per week. It costs 5500 e. Calculate the optimal production batch size? (5 points) f. What is the maximum inventory level achieved? (4 points)