A company's profit function, P(x), is given by the equation P(x) = 100x - 0.01x^2. Which of the following values of x represents the maximum possible profit?

Core Concept

To find the maximum possible profit, we need to find the critical point of the profit function P(x) = 100x - 0.01x^2. Taking the derivative of the function and setting it equal to 0, we get dP/dx = 100 - 0.02x = 0. Solving for x, we find x = 5000. However, the second derivative test reveals that x = 5000 is a local maximum, and x = 2500 is the absolute maximum. The correct answer is B) x = 2500. Options A, C, and D are incorrect because they do not represent the maximum possible profit.