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Question: Drinking water production

A worker currently works a total of $12$ hours a day for $240$ bottles of water. S$/$he thinks that with the use of a more practical and new label, S$/$he can increase the daily number of bottles up to $360$ bottles of water. The total material cost for each bottle of water is approximately $$3\mathrm{.}50$; needs to invest $$20$ per day in necessary materials; her$/$his energy costs are assumed to be only $$4\mathrm{.}00$ per day, and s$/$he figures $\frac{S}{?}$ he should earn $$10$ per hour for her$/$his time.

Looking at the above mentioned scenario from a total $($multi$-$factor$)$ productivity perspective and answer the following questions.

a$)$ What is the productivity of the relevant worker at this moment with the practical use of labels? $(10$ points$)$

b$)$ Explain whether the changes made were beneficial or not. $($You need to show calculations that support your explanation; for example, calculate the productivity growth rate$).(10$ points$)$

c$)$ What would the total $($multifactor$)$ productivity change be if the new practice increased material cost by $$0\mathrm{.}50$ per bottle of water with the use of labels? Explain briefly. $(20$ points$)$

d$)$ If it uses new and practical labels, how much can material costs increase without reducing total $($multi$-$factor$)$ productivity? Explain briefly. $(20$ points$)$

e$)$ Show the efficiency figures calculated in part $($a$)$ on the graph. Explain briefly.

$(20$ points$)$

f$)$ Let's assume that the inflation rate increases by $2\%$ when you start using new and practical labels. Calculate total factor productivity in case of $2\%$ inflation. Explain briefly. $(20$ points$)$