Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside$$s generator production operation, which is operated at a constant rate, will require $1000$ components per month throughout the year $(12,000$ units annually$).$ Assume that the ordering costs are $$25$ per order, the unit cost is $$2\mathrm{.}50$ per compo$-$ nent, and annual holding costs are $20\%$ of the value of the inventory. Westside has $250$ work$-$ ing days per year and a lead time of $5$ days. Answer the following inventory policy questions:

a$.$ What is the EOQ for this component?

b$.$ What is the reorder point?

c$.$ What is the cycle time?

d$.$ What are the total annual holding and ordering costs associated with your recom$-$

mended EOQ?