let x be the amount of tons of beans
- the price for 1 t of beans is (500 - 2x)
- the total revenue is
Expand the bracket, collect like terms:
You'll get the extreme value for r if r'(x) = 0
Btw: The graph of r is a parabola opening downward which has it's maximum as it's vertex. The x-coordinate of the vertex of a parabola is calculated by
. With your problem:
That means it isn't necessary to use calculus here.