Question

A produce distributor uses 777 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 37 percent of the purchase price per crate. Ordering costs are $25. Currently the manager orders once a month. How much could the firm save annually in ordering and carrying costs by using the EOQ? (Round intermediate calculations and final answer to 2 decimal places.)

Answer 1

The firm could save $16,227.24 annually by using the EOQ model, which optimizes the number of orders and reduces carrying costs.

Step-by-step explanation:

To calculate how much the firm could save annually by using the Economic Order Quantity (EOQ), we must first determine the EOQ itself using the formula:

`\[ \text{EOQ} = \sqrt{\frac{{2 * \text{Annual Demand} * \text{Ordering Cost}}}{{\text{Carrying Cost per Crate}}}} \]`

Given that the company uses 777 packing crates a month and orders once a month, the annual demand (D) is 777 crates × 12 months = 9,324 crates. The ordering cost (S) is $25 per order. The annual holding cost per unit (H) is 37% of the purchase price ($10), which amounts to $3.70 per crate.

Inserting these values into the EOQ formula gives us:

`\[ \sqrt{\frac{{2 * 9,324 * 25}}{{3.70}}} = \sqrt{\frac{{498600}}{{3.70}}} = √(134783.78) \approx \]`
`367.13`

EOQ =
`367.13` crates.

The optimal number of orders per year is then the total annual demand divided by EOQ, which is 9,324 / 367.13 ≈ 25.39, rounded to 26 orders per year.

If the firm orders 26 times a year instead of 12, the ordering cost will be 26 × $25 = $650, as opposed to the current $300 (12 × $25). The total holding costs with EOQ would be (EOQ/2) ×$3.70, equal to (367.13/2) × $3.70 ≈ $678.16. This is in comparison to the current holding cost of (777/2)×$3.70/12 = $1,437.95 per month or $17,255.40 per year.

Therefore, the annual savings by using EOQ would be the current total cost minus the EOQ total cost: ($300 + $17,255.40) - ($650 + $678.16) = $17,555.40 - $1,328.16 = $16,227.24.

So, by using the EOQ, the firm could save $16,227.24 annually.

Answer 2

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.