2021/‫‏‬6/‫‏‬29
Productivity Problems
Matthew W Ford
Productivity Practice Problems (Updated 10/11/2010 12:31 PM)
Courses:
MGT 305
MGT 307
MGT 415
MGT 490
FIN 450
Key relationship: productivity = output/resources used = output/input
1. FastCo has generated productivity data for the first two quarters of the year (Table 1). Using dollar
measures of input and output, compare the total profit and productivity achieved for the first two
quarters. How does Q2 productivity compare with Q1 productivity? Use partial factor productivity to
identify what might be done to improve productivity and profitability during Q3.
Table 1: FastCo Quarterly Productivity Data
Research
Q1
Q2
$20
$21
10,000
8,500
9,000
7,750
$10
$10
5,000
4,500
$15.00
$15.50
$20,000
$18,000
Unit selling price
Student
Resources:
Memos
ModelMemos
Resumes
% Diff
Tables
Graphs
Citations
Total units sold
Labor hours
Labor cost/hr
Material usage (lb)
Material cost/lb
Other costs
Solution:
QC .xls
Q1
Q2
$20*10,000=$200,000
$178,000
Input
$10*9000+$15*5000+$20,000=$185,000
$165,250
Profit
$200,000-$185,000=$15,000
$13,250
200,000/185,000=1.081
1.080 (-0.1%)
QCformulas
Output
Home
Productivity
Note: Are these partial-, multi-, or total factor productivities?
Profit decreased $1750 but productivity remained about the same (-0.1% year over year).
Looking at partial factor productivity for labor and materials:
Q1
Q2
Labor productivity
200,000/90,000=2.22
2.30 (+3.6%)
Material productivity
200,000/75,000=2.67
2.56 (-4.1%)
Labor productivity appears to have increased (+3.6%); material productivity appears to have decreased
(-4.1%).
https://www.nku.edu/~fordmw/producti.htm 1/2
2021/‫‏‬6/‫‏‬29
Productivity Problems
2. XYZ Manufacturing uses two measures of productivity: a) total sales/total inputs, b) total sales/total
labor inputs. Given data for the last three years (Table 2), calculate the productivity ratios. How would
you interpret the results.
Table 2: XYZ Productivity Data (in millions of dollars)
Y1
Y2
Y3
110
129
124
Materials
62
73
71
Labor
28
33
28
8
12
10
Sales
Overhead
Solution:
Y1
Y2
Y3
Total sales/total inputs
1.12
1.09 (-2.7%)
1.13 (+3.7%)
Total sales/total labor input
3.93
3.91 (-0.5%)
4.42 (+13.0%)
Total factor productivity and partial factor productivity with respect to labor, after decreasing in Y2, appears to have increased
in Y3.
Note: Which of the above is total factor productivity? Why?
3. A hamburger factory produces 50,000 burgers each week. The equipment costs $5,000 and will remain productive for three
years. The annual labor cost is $8,000.
a) What is the productivity as measured in units of output per dollar of input over a 3 year period?
b) Management has the option of $10,000 equipment, with an operating life of five years. It would reduce labor costs to $4,000
per year. Should management purchase this equipment (using productivity arguments alone)?
Solution:
a) In this case, define
productivity = (total burgers produced)/($labor+$equipment)=(50,000*52*3)/(8000*3+5000)
= 269 burgers/$input
b) for new machine project:
productivity=(50,000*52*5)/(4000*5+10,000)
=433 burgers/$input
This is a good project from a productivity perspective. Although the proposed equipment is expensive, 5 year life and lower
labor costs make new machine attractive.
NOTE: These problems are adapted from Evans, J.R. (1997). Production/Operations Management, 5th ed. Minneapolis/St.
Paul: West.
Site maintained 1999-2016 by Matthew W. Ford.
https://www.nku.edu/~fordmw/producti.htm 2/2