Math for Liberal Arts Calculus Word Problem

Question

The profit formula John Solar Panel Company is P= -40x^2 + 160000x. How many solar panels must they build and sell to maximize profit? What will the maximum profit be?

Answer 1

PROBLEM

Math for Liberal Arts Calculus Word Problem

The profit formula John Solar Panel Company is P= -40x^2 + 160000x. How many solar panels must they build and sell to maximize profit? What will the maximum profit be?

SOLUTION

The equation P = -40x² + 160000x is a quadratic of the form y = ax² + bx + c, where a = -40, b = 160000, and c = 0. The vertex (x, f(x)) is found from the formula x = -b/2a and y = f(-b/2a).

Therefore, the number of solar panels required to maximize profit, x = -(160000)/(2·-40) = 2000, and the maximum profit, P = -40(2000)² + 160000(2000) = 160000000.