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

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 $\_\_\_\_\_\_$

The answer is neither $2,284$ boxes not $6\mathrm{.}6$ orders per year :)