MBI is a manufacturer of personal computers. All its personal computers use a hard disk drive which it purchases from Ynos. MBI operates its factory 52 weeks per year, which requires assembling 100 of these disk drives into computers per week. MBI€™s annual holding cost rate is 20 percent of the value (based on purchase cost) of the inventory. Regardless of order size, the administrative cost of placing an order with Ynos has been estimated to be $50. A quantity discount is offered by Ynos for large orders as shown below, where the price for each category applies to every disk drive purchased.

T (a) Determine the optimal order quantity according to the EOQ model with quantity discounts. What is the resulting total cost per year?
(b) With this order quantity, how many orders need to be placed per year? What is the time interval between orders?

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Discount Category Quantity Purchased Price (per Disk Drive) 1 to 99 100 to 499 500 or more $100 95 90