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

Answer 1

$30

Explanation:

To answer this, maximize the profit function P(x)= -5x^2 + 300x + 15,000. Note that this is a quadratic function with coefficients -5, 300, 15000. Find the x-coordinate of the vertex: It is

-300

x = ------------ = 30, and because coefficient a is negative, we know that

2(-5) the graph opens downward and the max is at x = 30.

Conclusion: charging $30 for its product will maximize the profit.