# Economic Order Quantity (EOQ) | Practical Problems and Solutions Written by True Tamplin, BSc, CEPF®
Updated on October 7, 2021

## Problem 1

The John Equipment Company estimates its carrying cost at 15% and its ordering cost at \$9 per order. The estimated annual requirement is 48,000 units at a price of \$4 per unit.

Required:

1. What is the most economical number of units to order?
2. How many orders should be placed in a year?
3. How often should an order be placed?

### Solution

1. What is the most economical number of units to order?

Annual requirement = 48,000 units
Ordering cost = \$9 per order
Carrying cost = 15% of per-unit cost
Per unit cost = \$4 per unit 2. How many orders should be placed in a year?

= Annual requirement / EOQ
= 48,000 units / 1,200 units
= 40 orders

3. How often should an order be placed?

Frequency of orders = No. of days in one year / No. of orders
= 360 days / 40 orders
= 9 days

## Problem 2

To date, Raymond Bro. has been purchasing an item in lots of 900 units. This equates to a three-month supply. The cost per unit is \$12, the order cost is \$16 per order, and the carrying cost is 25%.

Required: How much can Raymond Bro. save per year by purchasing the item in the most economical quantities?

### Solution The first stage in our working is to compute the annual requirement.

Given that 900 units amounts to a three-month supply, the monthly requirement is 900 units / 3 months = 300 units.

Therefore, the annual requirement is 300 units x 12 months = 3,600 units.

In turn, the EOQ can be computed as follows: No. of Orders = 3,600 units / 900 units
= 4 orders
= 3,600 units / 196 units
= 18 orders approx.
Ordering Cost = 4 orders x \$16 per order
= \$64
Also, in the case of EOQ:
= 18 orders x \$16 per order
= \$288
Average Inventory = 900 units / 2
= 450 units
In the case of EOQ:
= 196 units / 2
= 98 units
Carrying cost = \$3 x 450 units
= \$1,350
In the case of EOQ:
= \$3 x 98 units
= \$294
Total cost = \$64 + \$1,350
\$1,414
In the case of EOQ:
=\$288 + \$294
= \$582
Saving = \$1,414 – \$582
= \$832

## Problem 3

A manufacturing company places a semi-annual order of 24,000 units at a price of \$20 per unit. Its carrying cost is 15% and the order cost is \$12 per order.

Required:

1. What is the most economical order quantity?
2. How many orders need to be placed?

### Solution No. of orders per year = Annual Requirement / EOQ
= 48,000 units / 620 units
= 77 orders approximately

To compute the annual requirement:

24,000 units are ordered semiannually, therefore:
Annual requirement = 24,000 units x 2 = 48,000 units.

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## About the AuthorTrue Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True contributes to his own finance dictionary, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University, where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website, view his author profile on Amazon, his interview on CBS, or check out his speaker profile on the CFA Institute website.

### 9 thoughts on “Economic Order Quantity (EOQ) | Practical Problems and Solutions”

1. The john equipment company estimates its carrying cost at 15% and its ordering cost at \$90 per order. The estimated annual requirement is 78,000 units at a price of \$4 per unit.
Required:
(i). What is the most economical no. of units to order?
(ii). No. of orders to be placed in a year.
(iii). About how often will an order need to be placed?
In the question annual requirement is given as 78000. But in answer it is taken as 48000 and the entire answer is wrong I think. Please don’t post such mistakes in publicly posted websites. We trust you and that is why we refer these questions and answers for quick reference. It
EOQ=Square root of (2*78000*9)/(4*15%)
The entire answer is wrong I think.

• That is exactly what I was thinking, but ordering cost was \$90 I suppose.
Thanks 🙂

2. EOQ=Square root of (2*78000*9)/(4*15%)
= Sqrt (1404000/.6)
=Sqrt (2340000)
=1529.71
Number of orders placed in an year=Annual consumption /EOQ
=78000/1529.71
=50.99
Frequency of orders=Number of days/Number of orders
=365/50.99
=7.16 days

• Aside the change of annual demand
The ordering cost is also changed
The final EOQ should be 4837 units

• Find EOQ if annual demand is 5000 units, ordering cost is Rs.125 per order and carrying cost
Rs.15 per unit.

3. He has just used 48000 in place of 78000, the approach is correct.

4. A company has an annual demand of 8000 units for an item. The supplier offers the units for sale at \$10.00 per unit for orders up to 500 units and at \$9.00 per unit for orders of 500 units or more. What is the economic order quantity if the order cost is \$30.00 per order and the holding cost rate is 30% per unit cost per year?

5. A gift shop sells Little Lentils—cuddly animal dolls stuffed with dried lentils—at a very
steady pace of 10 per day, 310 days per year. The wholesale cost of the dolls is \$5, and the
gift shop uses an annual interest rate of 20 percent to compute holding costs.
(a) If the shop wants to place an average of 20 replenishment orders per year, what order
quantity should it use?
(b) If the shop orders dolls in quantities of 100, what is the implied fixed order cost?
(c) If the shop estimates the cost of placing a purchase order to be \$10, what is the optimal
order quantity?

6. Consider the following inventory situation:
Period Starting inventory Ending inventory
Month 1 10 8
Month 2 8 6
Month 3 6 4
Month 4 4 2
Month 5 2 0

Suppose the following information is available:
Annual carrying cost 50 cent/unit
Order cost R10/order

Determine the following:
a. Optimal order quantity per order
b. Minimum total annual inventory costs
c. The number of orders per year
d. The time between orders (in working days)
i need help with this question please