The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by

q = −4p + 544,

where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue?

We have been given the demand equation for Turbos as [tex]q=-4p+544[/tex], where q is the number of buggies the company can sell in a month if the price is $p per buggy.

Let us find revenue function by multiplying price of p units by demand function as:

Revenue function: [tex]pq=p(-4p+544)[/tex]

[tex]pq=-4p^2+544p[/tex]

Since revenue function is a downward opening parabola, so its maximum point will be vertex.

Let us find x-coordinate of vertex using formula [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-b}{2a}=\frac{-544}{2\times -4}[/tex]

[tex]\frac{-b}{2a}=\frac{-544}{-8}[/tex]

[tex]\frac{-b}{2a}=68[/tex]

The maximum revenue would be the y-coordinate of vertex.

Let us substitute [tex]x=68[/tex] in revenue formula.

[tex]pq=-4(68)^2+544(68)[/tex]

[tex]pq=-4*4624+544(68)[/tex]

[tex]pq=-18496+36992[/tex]

[tex]pq=18496[/tex]

Therefore, the company should sell each buggy for $68 to get the maximum revenue of $18,496.