The annual demand for an item is $2,000$ units. The cost to process an order is $$75,$ and the annual

inventory holding cost is $20\%$ of item cost.

$($a$)$ What is the optimal order quantity, given the following price breaks for purchasing the item?

$($b$)$ What price should the firm pay per unit?

$($c$)$ What is the total annual cost at the optimal behavior, including purchasing cost?

Quantity Price

$1-499$ $$3\mathrm{.}00$ per unit

$500-999$ $$2\mathrm{.}50$ per unit

$1,000-4,999$ $$2\mathrm{.}25$ per unit

$5,000$ or more $$2\mathrm{.}00$ per unit