Economic Order Quantity. Micro-Encapsulator Corp. (MEC) expects to sell 7,200 miniature home encapsulators this year. The cost of placing an order from its supplier is $250. Each unit costs $50 and carrying costs are 20 percent of the purchase price.

Question

Economic Order Quantity. Micro-Encapsulator Corp. (MEC) expects to sell 7,200 miniature home encapsulators this year. The cost of placing an order from its supplier is $250. Each unit costs $50 and carrying costs are 20 percent of the purchase price.
What is the economic order quantity?
What are total costs—order costs plus carrying costs—of inventory over the course of the year?

GPT-4o mini · Answer

To calculate the Economic Order Quantity (EOQ) and the total costs (order costs plus carrying costs), we can use the following formulas.

Step 1: Calculate the Economic Order Quantity (EOQ)

The EOQ formula is given by:

\[ EOQ = \sqrt{\frac{2DS}{H}} \]

where:

$ D $ = annual demand (units per year)
$ S $ = ordering cost per order
$ H $ = holding (carrying) cost per unit per year

Given:

$ D = 7,200 $ units
$ S = 250 $ dollars per order
Purchase cost per unit = 50 dollars
Carrying cost percentage = 20% of the purchase price

First, we need to calculate the carrying cost ($ H $):

\[ H = \text{Carrying cost percentage} \times \text{Cost per unit} = 0.20 \times 50 = 10 \text{ dollars} \]

Now we can calculate EOQ:

\[ EOQ = \sqrt{\frac{2 \times 7200 \times 250}{10}} = \sqrt{\frac{3600000}{10}} = \sqrt{360000} = 600 \text{ units} \]

Step 2: Calculate Total Costs

Total costs consist of ordering costs and carrying costs.

2.1 Calculate Ordering Costs

The formula for total ordering costs is:

\[ \text{Total Ordering Costs} = \left(\frac{D}{Q}\right) \times S \]

Where $ Q $ is the EOQ.

Number of orders per year = $ \frac{D}{Q} = \frac{7200}{600} = 12 $

Thus, the total ordering costs are:

\[ \text{Total Ordering Costs} = 12 \times 250 = 3000 \text{ dollars} \]

2.2 Calculate Carrying Costs

The formula for total carrying costs is:

\[ \text{Total Carrying Costs} = \left(\frac{Q}{2}\right) \times H \]

Thus, the total carrying costs are:

\[ \text{Total Carrying Costs} = \left(\frac{600}{2}\right) \times 10 = 300 \times 10 = 3000 \text{ dollars} \]

Step 3: Calculate Total Inventory Costs

Finally, the total inventory costs are:

\[ \text{Total Costs} = \text{Total Ordering Costs} + \text{Total Carrying Costs} = 3000 + 3000 = 6000 \text{ dollars} \]

Summary of Results

Economic Order Quantity (EOQ): 600 units
Total Costs (Order Costs + Carrying Costs): 6000 dollars