Consider the crew productivity data shown in the following table. $(15$ points$)$

$\backslash$table$[[$Output$,$Crew$-$Hours$],[34,40],[36,42],[47,44],[48,46],[57,48],[59,50],[58,52],[60,54],[59,56],[59,58],[60,60]]$

a$)$ Develop a quadratic polynomial model to assess the productivity as a function of overtime hours worked.

b$)$ Does the model fit the data adequately? Why or why not?

c$)$ What is the normal work week $($i$.$e$.$ non$-$OT$)$ efficiency of this crew?

d$)$ For maximum productivity, what percentage of overtime should be worked?

e$)$ How many hours per week should the crew work?

f$)$ Do you think this level of effort is sustainable over time?

g$)$ Do you think this level of effort safe to work over time? Support your answers.