Chapter 16, Problem 1P

a)

Summary Introduction

To determine: The optimal order quantity per order.

Explanation of Solution

Given information:

It is given that the ordering cost (C_o) is $450, demand (D) is 1,200 units, and carrying cost (C_c) is $170.

Determine the optimal order quantity per order:

$\begin{array}{c}Q=\sqrt{\frac{2C_{o}D}{C_c}}\\ =\sqrt{\frac{2\times 450\times 1200}{170}}\\ =79.7\end{array}$

Hence, the optimal order quantity per order is 79.7 units.

b)

Summary Introduction

To determine: The minimum total annual inventory costs.

Explanation of Solution

Given information:

It is given that the ordering cost (C_o) is $450, demand (D) is 1,200 units, and carrying cost (C_c) is $170.

Determine the minimum total annual inventory costs:

$\begin{array}{c}TC=C_o\frac{D}{Q}+C_c\frac{Q}{2}\\ =450\left(\frac{1200}{79.7}\right)+170\left(\frac{79.7}{2}\right)\\ =6,775.4+6,774.5\\ =13,550\end{array}$

Hence, the minimum total annual inventory costs is $13,550.

c)

Summary Introduction

To determine: The optimal number of orders per year.

Explanation of Solution

Given information:

It is given that the ordering cost (C_o) is $450, demand (D) is 1,200 units, and carrying cost (C_c) is $170.

Determine the optimal number of orders per year:

$\begin{array}{c}\text{Optimal number of order}=\frac{D}{Q}\\ =\frac{1,200}{79.7}\\ =15.05\end{array}$

Hence, the optimal number of orders per year is 15.05 orders.

d)

Summary Introduction

To determine: The optimal time between orders.

Explanation of Solution

Given information:

It is given that the ordering cost (C_o) is $450, demand (D) is 1,200 units, and carrying cost (C_c) is $170.

Determine the optimal time between orders:

$\begin{array}{c}\text{Optimal time between orders}=\frac{\text{Number of working days}}{\text{Optimal number of orders}}\\ =\frac{364}{15.05}\\ =24.18\end{array}$

Hence, the optimal time between orders is 24.18 days.