Final answer:
The economic order quantity (EOQ) for the company is approximately 162 units, with an optimal number of orders per year of about 41. The total annual cost of operating the system is approximately $1956.
Step-by-step explanation:
The question involves the calculation of the Economic Order Quantity (EOQ), optimal number of orders per year, and the total annual cost of operating the system for a company. Given the parameters, it can be solved using the EOQ formula:
- Daily demand (d) = 18 units
- Holding cost per unit per year (h) = $12
- Ordering cost per order (s) = $24
- Annual demand (D) = 18 units/day * 365 days/year = 6570 units/year
The EOQ formula is given by:
EOQ = sqrt((2DS) / H)
Inserting the given values:
EOQ = sqrt((2 * 6570 * 24) / 12) = sqrt((314,160) / 12)
EOQ ≈ sqrt(26,180) ≈ 161.80 units
Therefore, the economic order quantity is approximately 162 units (rounded to the nearest whole number).
The optimal number of orders per year (N) = D / EOQ = 6570 / 162 ≈ 40.56 ≈ 41 orders/year
To find the total annual cost, we add the total holding cost and the total ordering cost:
Total holding cost = EOQ/2 * h
Total ordering cost = D/EOQ * s
Total annual cost = Total holding cost + Total ordering cost
Total annual cost ≈ (162/2 * 12) + (6570/162 * 24)
Total annual cost ≈ (81 * 12) + (41 * 24)
Total annual cost ≈ 972 + 984 = $1956
The total annual cost of operating the system is approximately $1956.