Rocky Mountain Tire Center sells $9,000$ go$-$cart tires per year. The ordering cost for each order is $$40,$ and the holding cost is $30\%$ of the purchase price of the tires per year. The purchase price is $$20$ per tire if fewer than $200$ tires are ordered, $$16$ per tire if $200$ or more, but fewer than $8,000,$ tires are ordered, and $$13$ per tire if $8,000$ or more tires are ordered.

a$)$ How many tires should Rocky Mountain order each time it places an order?

Rocky Mountain's optimal order quantity is units $($enter your response as a whole number$).$

b$)$ What is the total cost of this policy?

Toral annual cost of ordering optimal order size$=($round yout response to the nearest whole number$)$