Chapter 4, Problem 6PA

a)

Summary Introduction

To determine: The cost of direct labor for the bicycle.

Explanation of Solution

Given information:

Identification of bottleneck:

Worker 1 performs Step 1 and Step 2 with a total time of 50 seconds.

Worker 2 performs Step 3 and Step 4 with a total time of 60 seconds.

Worker 3 performs Step 5 with a time of 50 seconds.

Worker 4 performs Step 6 with a time of 45 seconds.

Worker 5 performs Step 7 with a time of 40 seconds.

Therefore, the bottleneck is Worker 2 with 60 seconds.

Calculation of cost of direct labor for the bicycle:

$\begin{array}{c}\text{Cost of direct labor}=\frac{\text{Number of workers}\times \text{Wage rate}}{\text{Bottleneck time}}\\ =\frac{5\times 15}{60}\\ =\frac{75}{60}\\ =\$1.25\text{ per bicycle}\end{array}$

The cost of direct labor per bicycle is $1.25.

b)

Summary Introduction

To determine: The profit per hour of the company.

Explanation of Solution

Given information:

Calculation of profit per hour:

The bottleneck time is 60 seconds. Therefore, 60 units are produced every hour. Therefore, the flow rate is 60 units per hour.

$\begin{array}{c}\text{Profit}=\text{Revenues}-\text{Cost}\\ \text{=}\left(\text{Flow rate}\times \text{Selling price}\right)-\left[\begin{array}{l}\left(\text{Number of workers}\times \text{Wage rate}\right)\\ +\left(\text{Flow rate}\times \text{Sourcing cost}\right)+\text{Fixed cost}\end{array}\right]\\ =\left(60\times \$6\right)-\left[\left(5\times \$15\right)+\left(60\times \$1\right)+\$200\right]\\ =360-\left[\left(75+60+200\right)\right]\\ =360-335\\ =\$25\text{ per hour}\end{array}$

The profit per hour is $25.

c)

Summary Introduction

To determine: The profit per hour of the company if the sourcing cost is 10% cheaper.

Explanation of Solution

Given information:

Calculation of profit per hour:

The bottleneck time is 60 seconds. Therefore, 60 units are produced every hour. Therefore, the flow rate is 60 units per hour.

$\begin{array}{c}\text{Profit}=\text{Revenues}-\text{Cost}\\ \text{=}\left(\text{Flow rate}\times \text{Selling price}\right)-\left[\begin{array}{l}\left(\text{Number of workers}\times \text{Wage rate}\right)\\ +\left(\text{Flow rate}\times \text{Sourcing cost}\right)+\text{Fixed cost}\end{array}\right]\\ =\left(60\times \$6\right)-\left[\left(5\times \$15\right)+\left(60\times \$0.90\right)+\$200\right]\\ =360-\left[\left(75+54+200\right)\right]\\ =360-329\\ =\$31\text{ per hour}\end{array}$

The profit per hour is $31.

d)

Summary Introduction

To determine: The profit per hour of the company if the fixed cost is 10% less.

Explanation of Solution

Given information:

Calculation of profit per hour:

The bottleneck time is 60 seconds. Therefore, 60 units are produced every hour. Therefore, the flow rate is 60 units per hour.

$\begin{array}{c}\text{Profit}=\text{Revenues}-\text{Cost}\\ \text{=}\left(\text{Flow rate}\times \text{Selling price}\right)-\left[\begin{array}{l}\left(\text{Number of workers}\times \text{Wage rate}\right)\\ +\left(\text{Flow rate}\times \text{Sourcing cost}\right)+\text{Fixed cost}\end{array}\right]\\ =\left(60\times \$6\right)-\left[\left(5\times \$15\right)+\left(60\times \$1\right)+\$180\right]\\ =360-\left[\left(75+60+180\right)\right]\\ =360-315\\ =\$45\text{ per hour}\end{array}$

The profit per hour is $45.

e)

Summary Introduction

To determine: The profit per hour of the company if the bottleneck time is reduced by 5 seconds per unit.

Explanation of Solution

Given information:

Calculation of profit per hour:

The bottleneck time is 55 seconds. Therefore, the flow rate is:

$\begin{array}{c}\text{Flow rate}=\frac{\text{60 Minutes}\times 60\text{ Seconds}}{\text{Bottleneck time}}\\ =\frac{60\times 60}{55}\\ =\frac{3,600}{55}\\ =65.45\text{}\text{ units per hour}\end{array}$

$\begin{array}{c}\text{Profit}=\text{Revenues}-\text{Cost}\\ \text{=}\left(\text{Flow rate}\times \text{Selling price}\right)-\left[\begin{array}{l}\left(\text{Number of workers}\times \text{Wage rate}\right)\\ +\left(\text{Flow rate}\times \text{Sourcing cost}\right)+\text{Fixed cost}\end{array}\right]\\ =\left(65.45\times \$6\right)-\left[\left(5\times \$15\right)+\left(65.45\times \$1\right)+\$200\right]\\ =392.7-\left[\left(75+65.45+200\right)\right]\\ =392.7-340.45\\ =\$52.25\text{ per hour}\end{array}$

The profit per hour is $52.25.