Question $4,$ Problem $12\mathrm{.}25$

Part $2$ of $2$

HW Score: $76\%,19$ of $25$ points

Points: $0$ of $6$

Rocky Mountain Tire Center sells $10,000$ go$-$cart tires per year. The ordering cost for each order is $$40,$ and the holding cost is $50\%$ of the purchase price of the tires per year. The purchase price is $$25$ per tire if fewer than $200$ tires are ordered, $$17$ per tire if $200$ or more $-$ but fewer than $5,000-$ tires are ordered, and $$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 $5,000$ 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 $=$$$157,580($round your response to the nearest whole number$).$