The revenue, R ( x ) , of producing and selling x Awesome Hearing Aids is modeled by the function R ( x ) = − 3 x^2 + 115 x

Question

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=-3x^2+115x

take the derivative and set equal to zero

R' = -6x+115 = 0

solve for x

6x=115

x=115/6 = 19 1/6 hearing aids

substitute back into the original R(x) equation

R=-3(115/6)^2+115(115/6)

=[-(1/12)+1/6](115^2)

= (1/6)(13225)

= 2204 1/6 is the maximum revenue

if that's dollars the it's $2204.17