Final answer:
By using the EOQ formula, the firm can determine the optimal order size. The EOQ is approximately 208.68 crates. By comparing the total costs, the firm could save approximately $712.02 annually in ordering and carrying costs by using the EOQ.
Step-by-step explanation:
The firm can calculate the Economic Order Quantity (EOQ) to determine the optimal order size that minimizes both ordering and carrying costs. The EOQ formula is:
EOQ = sqrt((2 * annual demand * ordering cost) / carrying cost per crate)
Using the given information, the annual demand is 777 crates, the ordering cost is $25, and the carrying cost is 37% of $10 per crate. Plugging these values into the formula, we get:
EOQ = sqrt((2 * 777 * 25) / (0.37 * 10))
Calculating this, the EOQ is approximately 208.68 crates.
To find the annual savings in ordering and carrying costs, we need to calculate the current total costs of ordering 777 crates at a time and compare it to the costs if the firm uses the EOQ. The total costs can be calculated as:
Total costs = (annual demand / EOQ) * ordering cost + (EOQ / 2) * carrying cost per crate
Using the current order size of 777 crates, the total costs are:
Total costs = (777 / 777) * 25 + (777 / 2) * (0.37 * 10)
Calculating this, the current total costs are $966.27. Now, using the EOQ of 208.68 crates, the total costs become:
Total costs = (777 / 208.68) * 25 + (208.68 / 2) * (0.37 * 10)
Calculating this, the EOQ total costs are $254.25. Therefore, the firm could save approximately $712.02 annually in ordering and carrying costs by using the EOQ.