Chapter 13, Problem 3P

A bakery buys flours 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 flow·.

C. If holding costs were to increase by $9 per year, how much would that affect the minimum total annual cost?

Summary Introduction

To determine:The Economic order quantity.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 3P

The Economic order quantity is 18 bags.

Explanation of Solution

Given information:

$\begin{array}{l}\text{D}=1,215\text{bags}\text{per}\text{year}\\ \text{S}=\text{\$10}\\ \text{H}=\text{\$75}\end{array}$

Formula:

${\text{Q}}_{\text{o}}=\sqrt{\frac{\text{2DS}}{\text{H}}}$

Calculation of Economic Order Quantity:

$\begin{array}{c}{\text{Q}}_{\text{o}}=\sqrt{\frac{\text{2}\times 1\text{,215}\times 10}{75}}\\ =18\text{bags}\end{array}$

The economic order quantity is calculated by dividing the product of 2 and 1,215 and 10 with 75 and taking square root which gives the resultant value as 18 bags.

Hence, the Economic order quantity is 18 bags.

Summary Introduction

To determine: The average number of bags on hand.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 3P

The average number of bags on hand is9 bags.

Explanation of Solution

Given information:

$\begin{array}{l}\text{D}=1,215\text{bags}\text{per}\text{year}\\ \text{S}=\text{\$10}\\ \text{H}=\text{\$75}\end{array}$

Calculation of average number of bags on hand:

$\begin{array}{c}\text{Average}\text{inventory}=\frac{\text{Q}}{\text{2}}\\ =\frac{18}{\text{2}}\\ =9\text{bags}\end{array}$

The average number of bags is hand is half of the economic order quantity which is 18 divided by 2 gives 9 bags.

Hence, the average number of bags on hand is 9 bags.

Summary Introduction

To determine:The number of orders per year.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 3P

The number of orders per yearis67.5 orders.

Explanation of Solution

Given information:

$\begin{array}{l}\text{D}=1,215\text{bags}\text{per}\text{year}\\ \text{S}=\text{\$10}\\ \text{H}=\text{\$75}\end{array}$

Calculation of number of orders per year:

$\begin{array}{c}\text{Number of order}\text{per}\text{year}=\frac{\text{D}}{\text{Q}}\\ =\frac{1,215\text{bags}}{18\text{bags/order}}\\ =67.5\text{orders}\end{array}$

The number of orders per year is calculated by dividing demand (1215 bags) with economic order quantity (18 bags/order) which is 67.5 orders.

Hence, the number of orders per year is 67.5 orders.

Summary Introduction

To determine:The total cost ordering and carrying flour.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 3P

The total cost ordering and carrying flouris$1,350.

Explanation of Solution

Given information:

$\begin{array}{l}\text{D}=1,215\text{bags}\text{per}\text{year}\\ \text{S}=\text{\$10}\\ \text{H}=\text{\$75}\end{array}$

Formula:

$\text{TC}=\left(\frac{\text{Q}}{\text{2}}\right)\text{H}+\left(\frac{\text{D}}{\text{Q}}\right)\text{S}$

Calculation of total cost:

$\begin{array}{c}\text{TC}=\left(\frac{18}{\text{2}}\right)75+\left(\frac{1,215}{18}\right)10\\ =\$675+\$675\\ =\$1,350\end{array}$

The cost is calculated by computing the ordering and carrying cost. The ordering cost is calculated by multiplying half of the EOQ with holding cost, 75 which results in $675. The carrying cost is calculated by dividing demand, 1215 with EOQ, 18 and multiplying the resultant with 10 which gives $675. The sum of both cost accounts to $1,350.

Hence, the total cost ordering and carrying flour is $1,350.

Summary Introduction

To determine: The total cost ordering and carrying flour.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 3P

The increase in cost is $78.71/year.

Explanation of Solution

Given information:

$\begin{array}{l}\text{D}=1,215\text{bags}\text{per}\text{year}\\ \text{S}=\text{\$10}\\ \text{H}=\text{\$75+9}=\text{\$84}\end{array}$

Formula:

$\text{TC}=\left(\frac{\text{Q}}{\text{2}}\right)\text{H}+\left(\frac{\text{D}}{\text{Q}}\right)\text{S}$

Calculation of total cost:

$\begin{array}{c}{\text{Q}}_{\text{o}}=\sqrt{\frac{\text{2}\times 1\text{,215}\times 10}{84}}\\ =17\text{bags}\end{array}$

The economic order quantity is calculated by dividing the product of 2 and 1,215 and 10 with 84 and taking square root which gives the resultant value as 17 bags.

$\begin{array}{c}\text{TC}=\left(\frac{17}{\text{2}}\right)84+\left(\frac{1,215}{17}\right)10\\ =\$714+\$714.71\\ =\$1,428.71\end{array}$

The cost is calculated by computing the ordering and carrying cost. The ordering cost is calculated by multiplying half of the EOQ with holding cost, 84 which results in $714. The carrying cost is calculated by dividing demand, 1215 with EOQ, 17 and multiplying the resultant with 10 which gives $714.71. The sum of both cost accounts to $1,428.71.

$\begin{array}{c}\text{Increase}\text{in}\text{cost}=\text{\$1,428}\text{.71-\$1,350}\\ =\text{\$78}\text{.71/year}\end{array}$

The increase in cost is the difference between $1,428 and $1,350 which gives $78.71/year.

Hence, increase in cost is $78.71/year.