The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function R(x) = -5 x^2 + 84 x....

Question

The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function
R(x) = -5 x^2 + 84 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) = -5x² + 84x

 

x = number of hearing aids produced/sold
R(x) = money made

 

This graphs as a parabola opening downward.

The maximum revenue is at the vertex of the parabola.

 

The vertex is at  (-b/2a, R(-b/2a))    a=-5,  b = 84

 

-b/2a = -84/2(-5) = -84/-10 = 8.4

R(8.4) = -5(8.4)² + 84(8.4) = $352.80

 

The problem shows a maximum revenue of $352.80 when

they produce and sell 8.4 Awesome Hearing Aids....

However; since they will not produce .4 hearing aids, one

needs to check the value at 8 and the value at 9...

 

R(8) = -5(8)² + 84(8) = $352

R(9) = -5(9)² + 84(9) = $351

 

In reality, the maximum revenue is $352 when 8 hearing

aids are produced and sold.  For purposes of the quadratic,

the maximum is $352.80 for 8.4 hearing aids.