A manufacturer has determined a cost function that expresses the annual cost of purchasing, owning, and maintaining its raw material inventory as a function of the size of each order. The cost function is C = 51200/q + 80q + 750000
where q equals the size of each order (in tons) and C equals the annual inventory cost.

a) Determine the order size q that minimizes annual inventory cost.

b) What are the minimum inventory costs expected to equal? $