Rocky Mountain Tire Center sells $7,000$ go$-$cart tires per year. The ordering cost for each order is $$35,$ and the holding cost is $40\%$ of the purchase price of the tires per year. The purchase price is $$21$ per tire if fewer than $200$ tires are ordered, $$18$ per tire if $200$ or more $-$ but fewer than $5,000-$ tires are ordered, and $$14$ per tire if $5,000$ 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$).$