$1-$ A component arrives gradually and at the rate of $20$ units per week and is used with the rate of $5$ units per week. The item costs $$2,000$ per unit. The cost per order is $$10,000$ and the annual holding cost is $\mathrm{.}25$ percent of the unit cost.

a$.$ Which inventory model should be used: EOQ $($Economic Order Quantity$)$ model or POQ $($Production Order Quantity$)$ model? Why?

b$.$ What is the optimal order quantity?

c$.$ What is the optimal annual ordering cost?

d$.$ What is the optimal annual holding cost?