Revenue The market research department of the Better Baby Buggy Co. predic...

Revenue The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = −0.5p + 140, where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? What is the largest monthly revenue? HINT [See Example 3.]

Example 3:

Alien Publications, Inc. predicts that the demand equation for the sale of its latest illustrated sci-fi novel Episode 93: Yoda vs. Alien is

q = −2,000p + 150,000

where q is the number of books it can sell each year at a price of $p per book. What price should Alien Publications, Inc., charge to obtain the maximum annual revenue?

Solution The total revenue depends on the price, as follows:

This value of p gives the highest point on the graph and thus gives the largest value of R(p). We may conclude that Alien Publications, Inc., should charge $37.50 per book to maximize its annual revenue.