As the logistics representative on a manufacturer's sales team, you have been asked to quantify the benefits that can be sold to a customer using more consistent service and transportation. The customer wants $99$ percent case availability from its distribution centers that are resupplied from the manufacturer. The average daily demand in cases from the customer's DC is $1,500$ units with a standard deviation of $250.$ Historically, the replenishment performance cycle has been $10$ days with a standard deviation of four days.The customer has traditionally used a $20$ percent inventory carrying cost, and the average value of each case is $$30.$ The customer orders weekly an order quantity of $7,000$ units.a$.$ What is the average inventory and annual carrying cost for the currentsituation?b$.$ What is the average inventory and carrying cost impact of reducing themanufacturer's performance cycle variation by $2$ days?c$.$ How does reducing the performance cycle variation by $2$ days comparewith reducing the average performance cycle length by $2$ days in terms ofaverage inventory and inventory carrying cost?