Total revenue and profit: This is a continuation . In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant but is, rather, a function of N. Suppose...

Total revenue and profit: This is a continuation . In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant but is, rather, a function of N. Suppose the manufacturer of widgets in has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.

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

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. Is R a linear function of N?

c. On the basis of the tables in this exercise and the preceding one, 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. Is P a linear function of N?