# Economic Order Quantity in a Bakery Business

## a) What is the Economic Order Quantity (EOQ) for a bakery that buys flour in 25 kg bags?

Options:

a) 139 bags

b) 140 bags

c) 138 bags

## b) How can we determine the average number of bags on hand in inventory?

## c) What is the expected number of orders per year for the bakery?

## d) How do we calculate the total annual cost of ordering and holding flour for the bakery?

## e) If ordering costs were to increase by 50 percent, by what percentage would the EOQ change?

## a) Economic Order Quantity (EOQ):

The EOQ for the bakery that buys flour in 25 kg bags can be calculated using the following formula:

EOQ = √((2 * D * S) / H)

Where:

D = Annual Demand in Units

S = Ordering Cost per Order ($10)

H = Annual Holding Cost per Unit ($5)

By substituting the values:

EOQ = √((2 * 4,860 * 10) / 5)

EOQ = √(19,440) ≈ 139.28

Therefore, the Economic Order Quantity (EOQ) is approximately 139 bags.

## b) Average Number of Bags on Hand:

The average number of bags on hand can be calculated as half of the EOQ:

Average number of bags on hand = EOQ / 2

Average number of bags on hand = 139 / 2 ≈ 69.5 bags

So, the bakery is expected to have approximately 69.5 bags on hand in inventory.

## c) Number of Orders per Year:

The number of orders per year can be determined by dividing the annual demand by the EOQ:

Number of Orders per Year = D / EOQ

Number of Orders per Year = 4,860 / 139 ≈ 34.89

Therefore, the bakery will need to place approximately 35 orders per year.

## d) Total Annual Cost of Ordering and Holding Flour:

The total annual cost of ordering and holding flour can be calculated by summing the ordering cost and the holding cost:

Total Annual Cost = (D / EOQ) * S + (EOQ / 2) * H

Substitute the values:

Total Annual Cost = (4,860 / 139) * 10 + (139 / 2) * 5

Total Annual Cost = 34.89 * 10 + 69.5 * 5

Total Annual Cost = $348.90 + $347.50

Total Annual Cost = $696.40

Hence, the total annual cost of ordering and holding flour for the bakery is $696.40.

## e) Impact of 50% Increase in Ordering Costs on EOQ:

If the ordering costs were to increase by 50%, the EOQ would be affected proportionally. The new EOQ value would change by the same percentage as the increase in ordering costs. In this case, the EOQ would increase by 50%, resulting in a higher quantity of bags to order for each batch.

In the bakery business, optimizing the order quantity and managing inventory effectively can significantly impact costs and operational efficiency. By understanding concepts like Economic Order Quantity (EOQ), businesses can make informed decisions to streamline their procurement processes.

The Economic Order Quantity (EOQ) helps in finding the optimal quantity of items to order that minimizes the total cost of ordering and holding inventory. It strikes a balance between ordering costs and holding costs, ensuring that the bakery maintains adequate stock levels without incurring unnecessary expenses.

Calculating the average number of bags on hand and the number of orders per year allows the bakery to plan its inventory management more efficiently. By knowing these figures, the bakery can schedule orders and deliveries effectively to meet customer demands while minimizing excess inventory and associated costs.

The total annual cost of ordering and holding flour provides a comprehensive view of the expenses incurred in managing inventory. By calculating this total cost, the bakery can assess its financial outlay and identify opportunities for cost savings and operational improvements.

In the scenario where ordering costs increase by 50%, the bakery would need to reassess its procurement strategy and adjust the EOQ accordingly. A higher EOQ would mean ordering larger quantities less frequently, potentially impacting storage space requirements and cash flow. It highlights the importance of monitoring and adapting to changes in cost factors to maintain cost-effectiveness in inventory management.