The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost
(a) What is the optimal order quantity, given the following price breaks for purchasing the item?
(b) What price should the firm pay per unit?
(c) What is the total annual cost at the optimal behavior?
Quantity Price
1-9 $2.95 per unit
10 - 999 $2.50 per unit
1,000 - 4,999 $2.30 per unit
5,000 or more $1.85 per unit
STEP 1: EOQ at $1.85 = 2013.47 → infeasible
EOQ at $2.30 = 1805.79 → feasible
So the possible best answers are 1806 and 5000
STEP 2: TC for 1806 units = $23,830.66
TC for 5000 units = $19,575.00
(a) Order 5000 units at a time.
(b) The price is $1.85 per unit.
(c) Total annual purchasing, holding, and setup costs = $19,575.00.
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