A small mail$-$order company uses $19,500$ boxes a year. Holding cost rate is $19$ percent of unit cost per year, and ordering cost is $$27$ per order. The following quantity discounts are available.

Number of Boxes Price per Box

$1,000$ to $1,999$ $$1\mathrm{.}20$

$2,000$ to $4,9991\mathrm{.}15$

$5,000$ to $9,9991\mathrm{.}10$

$10,000$ or more $1\mathrm{.}05$

a$.$ Determine the optimal order quantity.

Optimal order quantity $2,297$ Numeric Response $1.$Edit Unavailable. $2,297$ incorrect.boxes

b$.$ Determine the number of orders per year. $($Round the final answer to $1$ decimal place.$)$

No$.$ of orders per year $8\mathrm{.}4$ Numeric Response $2.$Edit Unavailable. $8\mathrm{.}4$ incorrect.