Assignment 1: Problem 1
A company that makes shopping carts for supermarkets recently purchased some new
equipment that reduced the labor content of the jobs needed to produce shopping
carts.
The information regarding the old system (before adding the new equipment) and after
adding the new equipment are given below.
Current System
Output/hr
80
Workers
5
Wage/hr
$10
Machine/hr
$40
New Equipment Added
84
4
$10
$50
a) Compute labor productivity for both the Old System and the New System
b) Compute AFP productivity for both the Old System and the New System
c) Suppose production with old equipment was 30 units of cart A at price of $100 per
cart, and 50 units of cart B at price of $120. Also suppose that production with new
equipment is 50 units of cart A, at price of $100 per cart, and 30 units of cart B at
price of $120. Compare all factor productivity for old and new systems.
Assignment 1: Problem 1
Output/hr
Workers
Wage/hr
Machine/hr
Current Situation
80
5
$10
$40
New Machine Added
84
4
$10
$50
(a) Compute labor productivity
Old System : 80/5 = 16 units/worker
New System : 84/4 = 21units/worker
(b) Compute all factor productivity
Old System : 80 / (5×10 + 40) = 0 .89 units/$
New System : 84 / (4×10 + 50) = 0.93 units/$
Assignment 1: Problem 1
(c) Now suppose:
Production with old equipment was 30 units of cart A at price of
$100 per cart, and 50 units of cart B at price of $120.
Production with new equipment is 50 units of cart A, at price of
$100 per cart, and 30 units of cart B at price of $120.
Compare all factor productivity for old and new systems.
AFP of the Old System =
[(30)(100)+(50)(120)] / [5×10 + 40] = 9000/90 = 100
AFP of the New System =
[(50)(100)+(30)(120)] / [4×10+50] = 8600/90 = 95.6
Assignment 1: Problem 2
A company has introduced a process improvement that reduces processing
time for each unit so that output is increased by 25% with less material
but one additional worker required.
Under the old process, five workers could produce 60 units per hour.
Labor costs are $12/hour, and material input was $16/unit.
For the new process, material is now $10/unit. Overhead is charged at
1.6 times direct labor cost.
Finished units sell for $31 each.
a)
b)
Compute single factor productivity of labor in the old system.
(Compute it in four possible ways.)
Compute all factor productivity for both old and new systems.
Factor
Output
Old System
60
New System
60(1.25) = 75
# of workers
Worker cost
Material
Overhead
Price
5
$12/hr
$16/unit
1.6(labor cost)
31
6
$12/hr
$10/unit
1.6(labor cost)
31
Problem 2; An additional computation
Factor
Output
# of workers
Worker cost
Material
Overhead
Price
Old System
60
5
$12/hr
$16/unit
1.6(labor cost)
31
New System
75
6
$12/hr
$10/unit
1.6(labor cost)
31
a) Compute labor productivity for the old system
Labor Productivity = 60/5 = 12 units per worker
Labor Productivity = [(60)(31)]/5 = 372 $ per worker
Labor Productivity = 60/[(5)(12)] = 1 unit per dollar
Labor Productivity = [(60)(31)]/[(5)(12)] = 31
Problem 2; AFP
Factor
Output
# of workers
Worker cost
Material
Overhead
Price
Old System
60
5
$12/hr
$16/unit
1.6(labor cost)
31
New System
75
6
$12/hr
$10/unit
1.6(labor cost)
31
b) Compute AFP
Since there is only a single output, in the numerator we can
have either # or $.
Since it is all factor productivity, in the denominator we must
have $
Problem 2; AFP
Factor
Output
# of workers
Worker cost
Material
Overhead
Price
Old System
60
5
$12/hr
$16/unit
1.6(labor cost)
31
New System
75
6
$12/hr
$10/unit
1.6(labor cost)
31
Old System
Denominator of all factor productivity is computed as
(5)(12) + (16)(60) + (1.6) (5)(12) = 1116
The numerator is (60)(31) = 1860
All factor productivity for old system = 1860/1116 = 1.67
New System
[(75)(31)]/ [(6)(12) + (10)(75) + (1.6) (6)(12)] = 2.48
1.67 in the old system, 2.48 in the new system
Assignment 1.3
3.
A milk factory seeks advice from an external consulting company concerning its
business and production processes. The final consulting report describes
several steps to increase productivity including implementation of cutting-edge
processing techniques through more powerful filtering systems.
Existing System
Proposed System
12
9
Milk Output/hour
1,000 gallons
1,400 gallons
Wage Rate/hour
$12
$12
Filtration Cost/hour
$120
$170
Workers
a)
b)
c)
Calculate the labor productivity for the existing as well as the proposed system.
Find the All-Factor Productivity for both systems.
Assume that current processing includes 700 gallons of Grade-A milk sold at
$2.40/gallon and 300 gallons of Grade-B milk at $1.90/gallon. Furthermore,
assume that under the proposed system, processing will include 600 gallons of
Grade-A milk at $2.40/gallon and 400 gallons of Grade-B milk at $1.90/gallon.
Compare all-factor productivity for both the existing and the new system.
8
Assignment 1.3
a)
Labor productivity for the existing system
Labor Productivity = 1000/12 = 83.33 gallons per worker
Labor Productivity = 1000/[(12)(12)] = 6.94 gallons per dollar
Labor productivity for the proposed system
Labor Productivity = 1400/9 = 155.56 gallons per worker
Labor Productivity = 1400/[(9)(12)] = 12.96 gallons per dollar
Assignment 1.3
b)
All factor productivity for the existing system
AFP = 1000/[(12)(12)+120] = 3.79 gallons per dollar
All factor productivity for the proposed system
AFP = 1400/[(9)(12)+170] = 5.04 gallons per dollar
Assignment 1.3
c. Existing system
700 gallons A @ $2.40/gallon = 1,680
300 gallons B @ $1.90/gallon = 570
12 labor @$12, $120 filtration
AFP (existing) = [1680+570/[(12*12)+120]
AFP (existing) = 2250/264= 8.52
c. Proposed system
600 gallons A @ $2.40/gallon = 1440
400 gallons B @ $1.90/gallon = 760
9 labor @$12, $170 filtration
AFP (proposed) = [1440+760]/[(9*12)+170]
AFP (proposed) = 2200/278=7.91