Rocky Mountain Tire Center sells 15,000 ​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 ​$25 per tire if fewer than 200 tires are​ ordered, ​$19 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 is the total cost of this​ policy?