$(1)(25$ points$)$ DDL produces a line of drives for personal computers. The drives use a $3\mathrm{.}5-$inch platter that DDL purchases from an outside supplier. Demand data and sales forecasts indicate that the weekly demand for the platters is closely approximated by a normal distribution with mean $200$ and variance $60.$ The platters require a five$-$week lead time for receipt. DDL has been using a $18\%$ annual interest charge to compute holding costs. The platters cost $$18$ each, fixed ordering cost is $$150$ per order, and the company is currently using a high stock$-$out cost of $$175$ per platter due to intense competition in the industry. a$)(5$ points$)$ DDL must purchase the platters in lots of $700$ due to a prior contract. What is the reorder point that the firm should be using in this case? b$)(10$ points$)$ When DDL renegotiates its contract with the supplier, what lot size should it write into the agreement? c$)(6$ points$)$ What is the total yearly cost $($setup$,$ holding and penalty$)$ of prior contract and the renegotiated contract? d$)(4$ points$)$ How much did service levels $($both type$-1$ and type$-2)$ improve after renegotiating the contract