A mail$-$order house uses $15,900$ boxes a year. Carrying costs are $48$ cents per box a year, and ordering costs are $$98.$ The following price schedule applies.

Number of Boxes $-$ Price per Box

$1,000$ to $1,999-$ $$1\mathrm{.}30$

$2,000$ to $4,999-1\mathrm{.}20$

$5,000$ to $9,999-1\mathrm{.}10$

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

a$.$ Determine the optimal order quantity. $($Round your answer to the nearest whole number.$)$

b$.$ Determine the number of orders per year. $($Round your answer to $2$ decimal places.$)$