More on revenue: This is a continuation of Exercises 11 and 12. 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...

More on revenue: This is a continuation of Exercises 11 and 12. 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. The total revenue R is still the product of p and N , but the formula for R is more complicated when p depends on N. Suppose the manufacturer of widgets in Exercises 11 and 12 no longer sells widgets for $25 each. Rather, the manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.

a. Verify that the formula p = 50 − 0.01N , where p is the price in dollars, gives the same values as those in the table.

b. Use the formula from part a and the fact that R is the product of p and N to find a formula expressing the total revenue R as a function of N for this widget manufacturer.

c. Express using functional notation the total revenue of this manufacturer if there are 450 widgets produced in a month, and then calculate that value.