Rocky Mountain Tire Center sells $14000$ go$-$cart tires per year. The ordering cost for each order is $$$$40,$ and the holding cost is $40\%$ of the purchase price of the tires per year. The purchase price is $$$$25$ per tire if fewer than $200$ tires are$$ ordered, $$$$19$ per tire if $200$ or more but fewer than $8000$ tires are$$ ordered, and $$$$15$ per tire if $8000$ or more tires are ordered.

Part $2$

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

Rocky$$ Mountain's optimal order quantity is$$

$8000$ units $($enter your response as a whole$$ number$).$

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

Total annual cost of ordering optimal order size$$$

$$

enter your response here $($round your response to the nearest whole$$ number$).$