The optimal order quantity that minimizes total annual cost is approximately 31 units.
To determine the optimal order quantity that minimizes the total annual purchasing, ordering, and holding cost, we need to consider the trade-off between ordering cost and holding cost. We can calculate the optimal order quantity using the Economic Order Quantity (EOQ) formula:
EOQ = √(2DS/H)
Where D is the demand per month, S is the ordering cost per order, and H is the holding cost as a percentage of the unit cost. In this case, D = 60 units per month, S = $40 per order, and H = 20% of $35 per unit. Plugging these values into the formula, we get:
EOQ = √(2 x 60 x 40 / (0.20 x 35))
Simplifying further, EOQ = √(4800 / 7) ≈ 31.17
Therefore, the optimal order quantity that minimizes the total annual cost is approximately 31 units.
Complete Question
Firm C's demand for a product is 60 units per month. Its supplier charges an ordering cost of $40 per order and $35 per unit with a 20% discount for orders of 100 units or more. Firm C incurs a 20% annual holding cost. What is the optimal order quantity that minimizes the total annual purchasing, ordering and holding cost?