A small mail$-$order company uses $15,000$ boxes a year. The holding cost rate is $20$ percent of unit cost per year, and the ordering cost is $$30$ per order. The following quantity discounts are available.

Number of Boxes Price per Box

$1\mathrm{.}000$ to $1\mathrm{.}9991\mathrm{.}30$

$2,000$ to $4,9991\mathrm{.}20$

$5,000$ to $9,9991\mathrm{.}18$

$10\mathrm{.}000$ or more $1\mathrm{.}16$

Determine the optimal order quantity.

$1000$

$5000$

@ $2000$

$10000$