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 $5,589$ units

Remember, for this $($and for all assignments this quarter$),$ you need to show your work. If you get the correct answer without showing your work, you may receive less than full credit.

a$)$ What is the productivity for each plant in each year?

Productivity for Plant A in $2015$: $10,500/80=131\mathrm{.}25$

Productivity for Plant B in $2015$: $3,840/32=120$

Productivity for Plant A in $2016$: $11,800/85=138\mathrm{.}82$

Productivity for Plant B in $2016$: $5,589/45=124\mathrm{.}2$

b$)$ Which plant is more productive in each year?

Plant A is more productive in each year because in $2015$ its $131\mathrm{.}25$ and year $2016$ is $138\mathrm{.}82.$

C$)$What was the productivity growth rate from $2015$ to $2016$ for each plant?

The Productivity growth rate for $2015$ to $2016$ for Plant A:

$(138\mathrm{.}82-131\mathrm{.}25)*100/131\mathrm{.}25=5\mathrm{.}76\%$

The Productivity growth rate for $2015$ to $2016$ for Plant B:

$(124\mathrm{.}2-120)*100/120=3\mathrm{.}5\%$

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 B surpasses Plant A: