Rocky Mountain Tire Center sells $11,000$go$-$cart tires per year. The ordering cost for each order is $$$$35,$ and the holding cost is $30\%$ of the purchase price of the tires per year. The purchase price is $$$$19$ per tire if fewer than $200$ tires are$$ ordered, $$$$17$ per tire if $200$ or more$$but fewer than $8,000$tires are$$ ordered, and $$$$13$ per tire if $8,000$ or more tires are ordered.

Part $2$

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

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