$3.$ The purchasing manager for Medco Research Laboratory orders letterhead forms and stationery from an office products firm in boxes of $500$ sheets. The company uses $5,000$ boxes per year. Annual carrying costs are $$4\mathrm{.}50$ per box, and ordering costs are $$34.$ The following all unit discount price schedule is provided by the office supply company:

Order Quantity $($boxes$)$ Price per Box

$200999$ $$13$

$1,0002,99912$

$3,0004,99911$

$5,000+10$

Determine the optimal order quantity and the total annual inventory cost.