A small mail$-$order company uses $16,000$ boxes a year. Holding cost rate is $16$ percent of unit cost per year, and ordering cost is $$31$ per order. The following quantity discounts are available.

Number of Boxes Price per Box

$1,000$ to $1,999$ $$1\mathrm{.}40$

$2,000$ to $4,9991\mathrm{.}35$

$5,000$ to $9,9991\mathrm{.}30$

$10,000$ or more $1\mathrm{.}25$

a$.$ Determine the optimal order quantity.

Optimal order quantity

boxes

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

No$.$ of orders per year