$[12$ Pts$]$ A manager has just received a revised price schedule from a vendor. What order

quantity should the manager use in order to minimize total costs? Annual demand is $150$

units, ordering cost is $$12,$ and annual carrying cost is $$1\mathrm{.}5$ per unit.

a$.[6$ Pts$]$ Determine the optimal order quantity and the total annual inventory cost.

b$.[6$ Pts$]$ Determine the optimal order quantity and total annual inventory cost if the

carrying cost is $20\%$ of the unit price.