1. A company has one item in its inventory that requires special storage. The co
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Question
1. A company has one item in its inventory that requires special storage. The company estimates the storage cost at $2.00 per unit per year. The demand for the item is 40,000 units per year, and the ordering cost is $16.00 per order. sion for the total yeary cost in terms of the order quantity Q, and determine the optimal order quantity Assuming shortages are allowed and cost $4.00 per unit per year, write an expression for the total yearly cost in terms of the order quantity Q and the maximum shortage level s, and determine the optimal order quantity b.Explanation / Answer
Given information, the company has one item in its inventory that requires special storage cost $2 per unit. The demand as 40,000 units per year, and the ordering cost of $16 per order
a) Total cost = holding cost + ordering cost
= (order quantity/2) x holding cost per unit per year + (annual demand/order quantity) x cost per order
Optimal order quantity (Q*) is found when annual holding cost = ordering cost
Q* = [2*Annual Demand* cost per order/holding cost per units per year]^0.5
Q* = [2*40000*16/2]^0.5 = (640000)^0.5 = 800
b) If shortages will be allowed we will have no holding cost
Total cost = ordering cost
= (annual demand/order quantity) x cost per order/shortages
Optimal order quantity (Q*) is found as
Q* = [Annual Demand* cost per order/4]^0.5
Q* = [40000*16*/4]^0.5 = (640000/4)^0.5 = 400
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