Chapter 7, Problem 5PA

a)

Summary Introduction

To determine: The maximum number horse sculptures that can be made in an hour.

Explanation of Solution

Given information:

Calculation of maximum number of horses:

Formula:

The maximum number of horse sculptures made in an hour is 4.8.

b)

Summary Introduction

To determine: The utilization % of the lathe.

Explanation of Solution

Given information:

Calculation of utilization of lathe:

Formula:

The utilization of lathe is 96%.

c)

Summary Introduction

To determine: The average inventory of body parts.

Explanation of Solution

Given information:

1 worker can assemble the horse sculpture in 16 minutes.

Calculation of flow rate:

$\begin{array}{c}\text{Flow rate}=\frac{\text{16 minutes}}{\text{60 minutes}}\\ =3.75\text{ sculptures per hour}\text{.}\end{array}$

Calculation of average inventory:

The total batch size of legs is 100 and the processing time is 4 minutes.

$\begin{array}{c}\text{Average inventory}=\frac{100\times \left[1-\text{Flow rate}\times \left(\frac{\text{Processing time}}{60\text{minutes}}\right)\right]}{2}\\ =\frac{100\times \left[1-3.75\times \left(\frac{4}{60}\right)\right]}{2}\\ =37.5\text{ body}\end{array}$

The average inventory is 37.5 body.

d)

Summary Introduction

To determine: The average inventory of leg parts.

Explanation of Solution

Given information:

1 worker can assemble the horse sculpture in 16 minutes.

Calculation of flow rate:

$\begin{array}{c}\text{Flow rate}=\frac{\text{16 minutes}}{\text{60 minutes}}\\ =3.75\text{ sculptures per hour}\text{.}\end{array}$

Calculation of average inventory:

The total batch size of legs is 400 and the processing time is 2 minutes.

$\begin{array}{c}\text{Average inventory}=\frac{400\times \left[1-\text{Flow rate}\times \left(\frac{\text{Processing time}}{60\text{minutes}}\right)\right]}{2}\\ =\frac{400\times \left[1-3.75\times \left(\frac{2}{60}\right)\right]}{2}\\ =100\text{ legs}\end{array}$

The average inventory is 100 legs.

e)

Summary Introduction

To determine: The number of body parts that needs to be made to minimize the inventory while not constraining the flow through the assembly.

Explanation of Solution

Given information:

1 worker can assemble the horse sculpture in 16 minutes.

Calculation of batch size:

The target capacity is the flow rate at 3.75 sculptures per hour. There is 1 body in each component set. Therefore, the batch size will be:

$\begin{array}{c}\text{Batch size}=\frac{\text{Target capacity}\times \frac{\text{Total setup time}}{60\text{ minutes}}}{1-\left(\text{Flow rate}\times \frac{\text{Processing time}}{60\text{ minutes}}\right)}\times 1\text{ Body part}\\ =\frac{3.75\times \frac{50}{60}}{1-\left(3.75\times \frac{12}{60}\right)}\times 1\\ =12.5\text{ body}\end{array}$

The body parts batch size is 12.5 body.

f)

Summary Introduction

To determine: The number of leg parts that needs to be made to minimize the inventory while not constraining the flow through the assembly.

Explanation of Solution

Given information:

1 worker can assemble the horse sculpture in 16 minutes.

Calculation of batch size:

The target capacity is the flow rate at 3.75 sculptures per hour. There is 4 body in each component set. Therefore, the batch size will be:

$\begin{array}{c}\text{Batch size}=\frac{\text{Target capacity}\times \frac{\text{Total setup time}}{60\text{ minutes}}}{1-\left(\text{Flow rate}\times \frac{\text{Processing time}}{60\text{ minutes}}\right)}\times 4\text{ Leg part}\\ =\frac{3.75\times \frac{50}{60}}{1-\left(3.75\times \frac{12}{60}\right)}\times 4\\ =50\text{ leg}\end{array}$

The leg parts batch size is 50 leg.