At Dot Com, a large retailer of popular books, demand is constant at $20,400$ books per year. The cost of placing an order to replenish stock is $$35,$ and the annual cost of holding is $$2\mathrm{.}00$ per book. Stock is received $12$ working days after an order has been placed. No backordering is allowed. Assume $275$ working days a year.

a$.$ Dot Com's optimal order quantity is ${845}^{TT}$ books. $($Enter your response rounded to the nearest whole number.$)$

b$.$ The optimal number of orders per year is orders. $($Enter your response rounded to the nearest whole number.$)$