Chapter 14.2, Problem 47E

Work the following applied problems. (See Example 5.)

Automobile Sales A car dealership estimates that the total weekly sales of its most popular model are a function of the car's list price p (in dollars) and the interest rate i (as a percent) offered by the manufacturer. The weekly sales are given by

$f\left(p,i\right)=99p-.5pi-.0025p^2.$

Find the weekly sales if the average list price is $p=\$19,400$ and the manufacturer is offering an 8% interest rate $\left(i=8\right)$.

Find and interpret $f_p\left(p,i\right)$ and $f_i\left(p,i\right)$.

What would be the approximate effect on weekly sales if the price is $19,400 and interest rates rise from 8% to 9%?