The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function R(x) = -4 x^2 + 51 x

Question

The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function
R(x) = -4 x^2 + 51 x

How many hearing aids need to be produced and sold in order to maximize the revenue? (Round to the nearest whole number.)

The revenue is at a maximum after____________ hearing aids are produced and sold.

What is the revenue? (Round answer to the nearest cent.)

The maximum revenue is $ _______

Answer 1

R'(x) = - 8x + 51 = 0; x = 51/8 = 6; R''(x) = - 8 < 0. So, we have max if x = 6 devices

The maximum revenue R(6) = - 4·36 + 51·6 = $162