explaining how to solve a problem: revenue from sales of tractors is function of...

[Please]

The John Deere Company has found thatthe revenue from sales of heavy-duty tractors is a function of the unit price pthat it charges. If the revenue R is R(p) = – 0.5p² + 1900p ,what unit price p should be charged to maximize revenue? What is the maximum revenue? Whatrecommendations would you give the John Deere Company?

I have explain this in detail and although I can solve it, I cant explain it well

 

[JeffM]

Can you post your solution: we'll check it.

We shall check it, and, if it is right, either Denis or I shall tell you how to explain it to people who have little knowledge and less interest in mathematics. We both have experience in that skill.

 

[HallsofIvy]

The simplest way to do this is to note that this is a quadratic "opening" downward. Its maximum is at its vertex. Find that vertex by "completing the square" so that the function is of the form "b- a(x- c)^2" where a is positive. Since a square is never negative, that is clearly "b minus something". That will take its largest value, b, when that "something" is 0.