Question $2.$ Disk Drives Limited $($DDL$)$ produces a line of internal Winchester disks for microcomputers. 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 seems to be closely approximated by a normal distribution with mean $38$ and variance during lead time is $390.$ The platters require a threeweek lead time for receipt. DDL has been using a $40$ percent annual interest charge to compute holding costs. The platters cost $$18\mathrm{.}80$ each, order cost is $$75\mathrm{.}00$ per order, and the company is currently using a stock$-$out cost of $$400\mathrm{.}00$ per platter. $($Because the industry is so competitive, stock$-$outs are very costly$.)$

a$.$ Because of a prior contractual agreement with the supplier, DDL must purchase the platters in lots of $500.$ What is the reorder point that it should be using in this case? $(6$ points$)$

b$.$ When DDL renegotiates its contract with the supplier, what lot size should it write into the agreement? $(15$ points$)$

c$.$ How much will the company save if applies the policy found in b$?(8$ points$)$

d$.$ DDL$\text{'}$s president is uncomfortable with the $$400$ stock$-$out cost and decides to substitute a $99$ percent fill rate criterion. What would its reorder point and the lot size be in this case? $(13$ points$)$