Chapter 1, Problem 5P

Summary Introduction

To determine: The productivity of Person GK and to know whether the organization is maintaining a manufacturing average of 3% increase in productivity every year.

Introduction: Productivity is a measure of the effectiveness of an individual, systems, machinery and other equipment that are used in converting inputs into outputs. In all organizations, productivity is an important determinant to know the cost efficiency.

Answer to Problem 5P

Person GK is maintaining the manufacturing average of a 3% increase in productivity per year in all the resources except capital.

Explanation of Solution

Given information: Person GK is producing bowling balls. The amount of resources used last year and in the current year is given as follows:

	Last year	Now
Units produced	1,000	1,000
Labor (hours)	300	275
Resin (pounds)	50	45
Capital invested ($)	10,000	11,000
Energy (BTU)	3,000	2,850

Formula to calculate productivity for last year and the current year:

$\text{Productivity}=\frac{\text{Total output}}{\text{Total input}}$

The productivity is calculated by dividing the total number of units produced by the total input used to produce the overall output.

Formula to calculate the change in the production units:

$\text{Change in production units}=\text{New productivity}-\text{Intital productivity}$

The change in production units are calculated by subtracting the current year’s productivity from the previous year’s productivity value.

Formula to calculate the percentage of productivity change:

$\text{Percentage change}=\frac{\text{Change in productivity}}{\text{Intital productivity}}$

The percentage change in productivity is calculated by dividing the change in productivity units by the initial productivity.

Substitution:

Resource	Last-year productivity	Current year productivity	Change in production units	Percentage of productivity change
Labor	3.33	3.64	0.30	9.01%
Resin	20.00	22.22	2.22	11.1%
Capital	0.10	0.09	-0.01	-10%
Energy	0.33	0.35	0.02	6.06%

Working note:

Calculate last-year productivity for labor:

The productivity is calculated by dividing the total number of units produced by the total input used to produce the overall output.

$\begin{array}{c}\text{Productivity}=\frac{\text{Total output}}{\text{Total input}}\\ =\frac{1,000}{300}\\ =3.33\end{array}$

Calculate last-year productivity for resin:

The productivity is calculated by dividing the total number of units produced by the total input used to produce the overall output.

$\begin{array}{c}\text{Productivity}=\frac{\text{Total output}}{\text{Total input}}\\ =\frac{1,000}{50}\\ =20\end{array}$

Note: The calculation continues for capital and energy.

Calculate current year productivity for labor:

The productivity is calculated by dividing the total number of units produced by the total input used to produce the overall output.

$\begin{array}{c}\text{Productivity}=\frac{\text{Total output}}{\text{Total input}}\\ =\frac{1,000}{275}\\ =3.64\end{array}$

Calculate current year productivity for resin:

The productivity is calculated by dividing the total number of units produced by the total input used to produce the overall output.

$\begin{array}{c}\text{Productivity}=\frac{\text{Total output}}{\text{Total input}}\\ =\frac{1,000}{45}\\ =22.22\end{array}$

Note: The calculation continues for capital and energy.

Calculate the change in the production units for labor:

The change in production units are calculated by subtracting the current year’s productivity from the previous year’s productivity value.

$\begin{array}{c}\text{Change in production units}=\text{Current year productivity}-\text{last-year productivity}\\ =3.64-3.33\\ =0.30\end{array}$

Calculate the change in the production units for resin:

The change in production units are calculated by subtracting the current year’s productivity from the previous year’s productivity value.

$\begin{array}{c}\text{Change in production units}=\text{Current year productivity}-\text{last-year productivity}\\ =22.22-20\\ =2.22\end{array}$

Note: The calculation continues for capital and energy.

Calculate the percentage of productivity change for labor:

The percentage change in productivity is calculated by dividing the change in productivity units by the initial productivity.

$\begin{array}{c}\text{Percentage change}=\frac{\text{Change in productivity}}{\text{Last-year productivity}}\\ =\frac{0.30}{3.33}\times 100\\ =9.01\%\end{array}$

Calculate the percentage of productivity change for resin:

The percentage change in productivity is calculated by dividing the change in productivity units by the initial productivity.

$\begin{array}{c}\text{Percentage change}=\frac{\text{Change in productivity}}{\text{Last-year productivity}}\\ =\frac{2.22}{20}\times 100\\ =11.1\%\end{array}$

Note: The calculation continues for capital and energy.

Hence, Person GKis maintaining the manufacturing average of a 3% increase in productivity per year in all the resources except capital.