Chapter 4, Problem 7PA

a)

Summary Introduction

To determine: The labor content.

Explanation of Solution

Given information:

Labor content:

The labor content is total time required to perform all the tasks of by the workers. It is 215 seconds.

The labor content is 215 seconds.

b)

Summary Introduction

To determine: The cost of direct labor for a toothbrush.

Explanation of Solution

Given information:

Calculation of time per worker:

The time for Worker A is 65 seconds.

The time for Worker B is 35 seconds.

The time for Worker C is 25 seconds.

The time for Worker D is 30 seconds.

The time for Worker E is 60 seconds.

The bottleneck is Worker A with 65 seconds. Therefore, the flow rate will be:

$\begin{array}{c}\text{Flow rate}=\frac{\text{60 minutes}\times 60\text{ seconds}}{\text{Bottleneck time}}\\ =\frac{60\times 60}{65}\\ =55.38\\ =55.4\text{ brushes per hour}\end{array}$

Cost of direct labor:

$\begin{array}{c}\text{Cost of direct labor}=\frac{\text{Wage rate}\times \text{Number of workers}}{\text{Flow rate}}\\ =\frac{\$15\times 5}{55.4}\\ =\frac{75}{55.4}\\ =\$1.35\end{array}$

The cost of direct labor per toothbrush is $1.35.

c)

Summary Introduction

To determine: The utilization of worker A.

Explanation of Solution

Given information:

Utilization of Worker A:

The time for Worker A is 65 seconds. It is the bottleneck time of the entire process. Therefore, the utilization is 100%.

The utilization of 100%.

d)

Summary Introduction

To determine: The average labor utilization of the process.

Explanation of Solution

Given information:

Average labor utilization of the process:

The cycle time will be equal to the bottleneck time which is 65 seconds. The average labor utilization will be:

$\begin{array}{c}\text{Average labor utilization}=\frac{\text{Total time}}{\text{Number of workers}\times \text{Cycle time}}\times 100\\ =\frac{215}{5\times 65}\times 100\\ =\frac{215}{325}\times 100\\ =66.15\%\end{array}$

The average labor utilization of 66.15%.

e)

Summary Introduction

To determine: The Takt time.

Explanation of Solution

Given information:

Demand rate = 40 toothbrushes per hour

Takt time:

$\begin{array}{c}\text{Takt time}=\frac{\text{Minutes per hour}\times \text{Seconds per minute}}{\text{Demand rate per hour}}\\ =\frac{\text{60}\times \text{60}}{\text{40}}\\ =90\text{ seconds}\end{array}$

The Takt time is 90 second per toothbrush.

f)

Summary Introduction

To determine: The target manpower.

Explanation of Solution

Given information:

Takt time = 50 seconds

Target manpower

$\begin{array}{c}\text{Target manpower}=\frac{\text{Total time}}{\text{Takt time}}\\ =\frac{215}{50}\\ =4.3\end{array}$

The target manpower is 4.3 workers.

g)

Summary Introduction

To determine: The capacity of the process after hiring the new worker.

Explanation of Solution

Given information:

New capacity of the process:

The new worker is added to Task 1 and Task 2 as it is the bottleneck of the process. After the addition of the new worker, the bottleneck is Worker E with a total time of 60 seconds. Therefore, the new capacity will be:

$\begin{array}{c}\text{Capacity}=\frac{\text{60 minutes}\times 60\text{ seconds}}{\text{Bottleneck time}}\\ =\frac{60\times 60}{60}\\ =60\text{ toothbrushes per hour}\end{array}$

The capacity of process is 60 toothbrushes per hour.

h)

Summary Introduction

To determine: The capacity of the process.

Explanation of Solution

Given information:

New capacity of the process:

The tasks are assigned to minimize the maximum work across the various workers. Task 1 is assigned to Worker A. Tasks 2, 3 is assigned to Worker B. Tasks 4, 5, 6, and 7 is assigned to Worker C. Tasks 8, 9 is assigned to Worker D. Task 10 is assigned to Worker E. The bottleneck time now is Worker 3 with 50 seconds. Therefore, the capacity is:

$\begin{array}{c}\text{Capacity}=\frac{\text{60 minutes}\times 60\text{ seconds}}{\text{Bottleneck time}}\\ =\frac{60\times 60}{50}\\ =72\text{ toothbrushes per hour}\end{array}$

The capacity of process is 60 toothbrushes per hour.

i)

Summary Introduction

To determine: The capacity of the process with the new method

Explanation of Solution

Given information:

New capacity of the process:

$\begin{array}{c}\text{Capacity}=\frac{\text{Number of workers}\times \text{60 minutes}\times 60\text{ seconds}}{\text{Total process time}}\\ =\frac{5\times 60\times 60}{215}\\ =83.7\text{ toothbrushes per hour}\end{array}$

The capacity of process is 83.7 toothbrushes per hour.