The table below contains production data from two facilities making the identical part. Plant APlant BAverage $2015$ workforce$80$ workers$32$ workersTotal $2015$ production$10,500$ units$3,840$ unitsAverage $2016$ workforce$85$ workers$45$ workersTotal $2016$ production$11,800$ units$5,859$ 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? 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.