A local distributor for a national tire company expects to sell approximately $10,110$ tires of a certain size and tread design next year. Annual carrying cost is $$15$ per tire and ordering cost is $$77.$ The distributor operates $283$ days a year. a$.$ What is the EOQ? b$.$ How many times per year does the store reorder? $($Round your answer to two decimal points.$)$ c$.$ What is the length of an order cycle? $($Round your answer to two decimal points.$)$ d$.$ What will the total annual carrying and ordering cost be if the EOQ quantity is ordered? $($Round your answer to a whole number.$)$