(30 points) Consider the following deterministic EOQ inventory model where no shortages are allowed with constant demand d = 2,000 per month and lead time L = 0.25 month. The purchase cost is cu = $100/item if the purchase quantity is less than q = 4,800 items, and c2 = $80/item if the purchase quantity is 4,800 items or more. The ordering cost is K = $50,000/order and holding cost per item per month is h = $10. The inventory manager uses the (R,Q) policy. a) (15 points) Find the optimal order quantity Q and the reorder level R that minimizes the average cost per month? b) (10 points) What is your answer to part a) if the holding cost per item per month is hi = $10 if the purchase cost is $100/item and h2 = $8 if the purchase cost is $80/item? Explain why. c) (5 points) Suppose that the demand during the lead time is random so that there can be shortages. Find the reorder level R such that 90% of the demand is satisfied on time if the demand during the lead time has the exponential distribution with mean 500