Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a
widget at which N widgets can be sold.

\(\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 200 & 53.00\\ \hline 250 & 52.50\\\hline 300 & 52.00\\ \hline 350 & 51.50\\ \hline \end{array}\)

(a) Find a formula for p in terms of N modeling the data in the table.

\(\displaystyle{p}=\)

(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.

\(\displaystyle{R}=\)

Is R a linear function of N?

(c) On the basis of the tables in this exercise and using cost, \(\displaystyle{C}={35}{N}+{900}\), use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.

\(\displaystyle{P}=\)

(d) Is P a linear function of N?