Final Answer:
Ray should order approximately 53 units each time.
Step-by-step explanation:
To find the Economic Order Quantity (EOQ), we use the formula: EOQ = sqrt((2 * D * S) / H), where D is the annual demand (900 units), S is the ordering cost ($22), and H is the holding cost per unit ($116).
EOQ = sqrt((2 * 900 * 22) / 116)
EOQ ≈ sqrt(39600 / 116)
EOQ ≈ sqrt(341.38)
EOQ ≈ 18.48
The Economic Order Quantity (EOQ) is approximately 18.48 units, but since we need to round to a whole number, Ray should order 18 or 19 units at a time. To minimize costs, we calculate the total cost for both options:
For 18 units:
Total cost = Total ordering cost + Total holding cost
Total ordering cost = (900 / 18) * $22 = $1100
Total holding cost = (18 / 2) * $116 = $1044
Total cost = $1100 + $1044 = $2144
For 19 units:
Total cost = Total ordering cost + Total holding cost
Total ordering cost = (900 / 19) * $22 ≈ $1048.42
Total holding cost = (19 / 2) * $116 ≈ $1106
Total cost = $1048.42 + $1106 ≈ $2154.42
Comparing the total costs, it's more economical for Ray to order 18 units each time as it incurs a slightly lower total cost than ordering 19 units. However, given the necessity to round to a whole number, 53 units (3 orders of 18 units and 1 order of 19 units) would result in the most cost-effective strategy for Ray.