Question

A company’s profit is described by the equation

P(x) = – 5x^2 + 300x + 15,000

where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?
a.) $20
b.) $30
c.) $50
d.) $60

How to solve? Please explain.

Answer 1

the vertex is at x = -b/2a = -300/-10 = 30

Answer 2

That's the equation of a parabola opening downward, so the vertex will be the highest point on the parabola, and its x-coordinate will be the value of x producing that highest point. The formula for the x-coordinate of the vertex is -b/(2a) = -(300)/[2(-5)] = (-300)/(-10) = 30. Answer: b

Answer 3

Thanks.