Rocky Mountain Tire Center sells $14,000$ go$-$cart tires per year. The ordering cost for each order is $$35,$ and the holding cost is $50\%$ of the purchase price of the tires per year. The purchase price is $$24$ per tire if fewer than $200$ tires are ordered, $$18$ per tire if $200$ or more, but fewer than $5,000,$ tires are ordered, and $$13$ 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$).$

b$)$ What iw the total cpst of this policy?

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

Please make sure it is correct and answer a$,$b