Cress Electronic Products manufactures components used in the automotive industry. Cress purchases parts for use in its manufacturing operation from a variety of different suppliers. The annual demand is $5000$ units, the ordering cost is $$80$ per order, and the annual holding cost rate is $25\%.$

a$.$ If the cost of the part is $$20$ per unit, what is the economic order quantity?

b$.$ Assume $250$ days of operation per year. If the lead time for an order is $12$ days, what is the reorder point?

c$.$ What is the total cost of this inventory system.

d$.$ Find the cycle time and the number of times an order will be placed in a year.