Rocky Mountain Tire Center sells $11,000$ 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 $$24$ per tire if fewer than $200$ tires are ordered, $$16$ 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$).$ Wrong answers will be downvoted and reported