A$).$ A part is produced in batches size of $2,500$ pieces. Annual demand is $35,000$ pieces, and piece cost is $$8\mathrm{.}50.$ Setup time to run a batch is $1\mathrm{.}5$ hr$,$ cost of downtime on the affected equipment is figured at $$200/$hr$,$ and annual holding cost rate is $18\%.$ What would the annual savings be if the product were produced in the economic order quantity? $(4+4+4+2$ marks$)$

B$).$ A company manufactures and sells a seasonal product. Based on the sales forecast that follows, calculate a level production plan, quarterly ending inventories, and average quarterly inventories. Assume that the average quarterly inventory is the average of the starting and ending inventory for the quarter. If inventory carrying costs are $$3$ per unit per quarter, what is the annual cost of carrying this anticipation inventory? Opening and ending inventories are zero $(11$ marks$)$