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1. A company has one item in its inventory that requires special storage. The co

ID: 1114160 • Letter: 1

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