Suppose *x* denotes the number of units a company plan to produce or sell,
usaually, a revenue function *R*(*x*) is set up as follows: *R*(*x*)=( price per
unit) (number of units produced or sold). Sometimes the price per
unit is a function *x*, say, *p*(*x*). It is often called a demand function
too because when a company produce (or sell) more, it means there is more
demand for the prouct, and the price per unit should come down. Let's see
the following

Example: A fast-food restaurant has determind that the monthly demand for
their hamburgers is given by * p(x) = (60,000-x)/20,000 *. (a) Find the
number of hamburgers this restaurant should sell in order that the revenue
is maximized. (b) Find the maximum revenue. (c) When will the restaurant
make no revenue at all?

We first set up the revenue function * R(x) = x[(60,000-x)/20,000] =
-x ^{ 2 }/20,000 + 3x *

Notice that *y*=*R*(*x*) is a parabola opening downward,
it has a maximum at * x = 30,000 * In other words, when the restaurant
sells 30,000 hamburgers. The maximum revenue is * R(30,000)=$45,000.
* And the restaurant makes
no revenue when *R*(*x*)=0, which means * -x ^{
2}/20,000 + 3x =0.* Using factoring
technique, we get

Wed Oct 30 21:29:01 EST 1996