The table below contains production data from two facilities making the identica
ID: 3144118 • Letter: T
Question
The table below contains production data from two facilities making the identical part.
Plant A
Plant B
Average 2015 workforce
80 workers
32 workers
Total 2015 production
10,500 units
3,840 units
Average 2016 workforce
85 workers
45 workers
Total 2016 production
11,800 units
5,859 units
a) What is the productivity for each plant in each year?
b) Which plant is more productive in each year?
c) What was the productivity growth rate from 2015 to 2016 for each plant?
d) Assume the growth rates you calculate in part c) continue into the future. For example, if you calculated growth from 2015 to 2016 as 20% for plant A and 15% for plant B, then assume productivity for each plant continues to grow at their respective rates for each subsequent year. In what year (if at all) does the less productive plant surpass the more productive plant (i.e. if this were a race in which the higher productivity plant wins, in what year does the plant which is currently trailing “take the lead”)? Note that I am asking about productivity, not output.
Plant A
Plant B
Average 2015 workforce
80 workers
32 workers
Total 2015 production
10,500 units
3,840 units
Average 2016 workforce
85 workers
45 workers
Total 2016 production
11,800 units
5,859 units
Explanation / Answer
(a) Productivity for each plant and each year are caluculated below
Productivity for plant A in 2015 = Total 2015 production in plant A / Average 2015 workforce in plant A
= 10500 / 80
= 131.25
Productivity for plant B in 2015 = Total 2015 production in plant B / Average 2015 workforce in plant B
= 3840/32
= 120
Productivity for plant A in 2016 = Total 2016 production in plant A / Average 2016 workforce in plant A
= 11800/85
= 138.82
Productivity for plant B in 2016 = Total 2016 production in plant B / Average 2016 workforce in plant B
= 5859/45
= 130.2
(b) By the above values we can say that PLANT A is more productive in both the years 2015 and 2016 as 131.25 and 138.82 respectivily.
(c) Productivity growth rate for plant A in 2015 to 2016 = (Productivity in plant A for 2016 - Productivity in plant A in for 2015) *100 /Productivity in plant A for 2015
= (138.82-131.25)*100/131.25
= 5.76 %
Productivity growth rate for plant B in 2015 to 2016 = (Productivity in plant B for 2016 - Productivity in plant B in for 2015) *100 /Productivity in plant B for 2015
= (130.2-120)*100/120
= 8.5 %
So the productivity growth rates from 2015 to 2016 for plant A and plant B are 5.76% and 8.5% respectivily.
(d) When plant B crosses plant A :
Let n be the number of year from 2016 in which plant B crosses the plant A productivity, and let take productivity of plants in 2016 in consideration for caluculations
Therefore 138.82 (1+0.0576)^n = 130.2 (1+0.085 )^n
n = ln(138.82/130.2)/ln(1.085/1.0576)
= 2.50
~ 3
So after 3 years from 2016 that is by 2019 the productivity of plant B crosses the productivity of plant A .
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