Question: 2) (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

2) (30 points) Consider the following deterministic EOQ inventory model where

2) (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 ci = $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 ? 2) (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 ci = $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

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