Calculus Optimization

Question

What is the maximum value of the product P = xy when

y = 2 - 5x?

Answer 1

Since y = 2 - 5x, P = xy = x(2 - 5x) = -5x² + 2x

The graph of P is a parabola opening downward with maximum when x = -2/[2(-5)] = 1/10

Maximum value of P is (1/10)[2 - 5(1/10)] = (1/10)(3/2) = 3/20.