Question

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?

Answer 1

Answer:

$68

Step-by-step explanation:

We have been given the demand equation for Turbos as $q=-4p+544$, 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: $pq=p(-4p+544)$

$pq=-4p^2+544p$

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

Let us find x-coordinate of vertex using formula $\frac{-b}{2a}$.

$\frac{-b}{2a}=\frac{-544}{2\times -4}$

$\frac{-b}{2a}=\frac{-544}{-8}$

$\frac{-b}{2a}=68$

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

Let us substitute $x=68$ in revenue formula.

$pq=-4(68)^2+544(68)$

$pq=-4*4624+544(68)$

$pq=-18496+36992$

$pq=18496$

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