Question

Problem 2 A bakery buys flour in 25-pound bags. The bakery uses 1,215 bags a year. Ordering cost is $10 per order, Annual carrying cost is $75 per bag. a. Determine the economic order quantity. b. What is the average number of bags on hand? c. How many orders per year will there be? d. Compute the total cost of ordering and carrying flour. e. If holding costs were to increase by $9 per year, how much would that affect the minimum total annual cost?

Answer 1

Answer:

Explanation:

a. The computation of the economic order quantity is shown below:

= $\sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}$

= $\sqrt{\frac{2\times \text{1,215}\times \text{\ 10}}{\text{\ 75}}}$

= 18 bags

b. The average inventory would equal to

= Economic order quantity ÷ 2

= 18 bags ÷ 2

= 9 bags

c. The number of orders would be equal to

= Annual demand ÷ economic order quantity

= $1215 ÷ 18 bags

= 67.5 orders

d. The total cost of ordering cost and carrying cost equals to

Ordering cost = Number of orders × ordering cost per order

= 67.5 orders × $10

= $675

Carrying cost = average inventory × carrying cost per unit

= 9 bags × $75

= $675

So, the total would be  

= $675 + $675

= $1,350

Now if holding cost is increased by $9, the holding cost would be 84

So,

a. The computation of the economic order quantity is shown below:

= $\sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}$

= $\sqrt{\frac{2\times \text{1,215}\times \text{\ 10}}{\text{\ 84}}}$

= 17 bags

b. The average inventory would equal to

= Economic order quantity ÷ 2

= 17 bags ÷ 2

= 8.5 bags

c. The number of orders would be equal to

= Annual demand ÷ economic order quantity

= $1215 ÷ 17 bags

= 71.47 orders

d. The total cost of ordering cost and carrying cost equals to

Ordering cost = Number of orders × ordering cost per order

= 71.47 orders × $10

= $714.70

Carrying cost = average inventory × carrying cost per unit

= 8.5 bags × $84

= $714

So, the total would be  

= $714.70 + $714

= $1,428.70

So, it would increase by

= $1,428.70 - $1,350

= $78.70