Price = x
Quantity = 200 - 3x
The formula for revenue is Price x Quantity. To be able to get the maximum revenue, let's multiply the price of each coffee maker and the number of coffee makers sold each week.
[tex]\begin{gathered} R=P\times Q \\ R=x(200-3x) \\ R=200x-3x^2 \end{gathered}[/tex]
The formula for the revenue as we can see above is R = 200x - 3x². To be able to solve for the maximum revenue, let's solve for the vertex of this quadratic equation.
The formula for the vertex is:
[tex]x=-\frac{b}{2a}[/tex]
where b = the first degree term and a = second degree term.
On our equation, our a = -3, and b = 200. Let's plug it in to our formula above.
[tex]x=-\frac{200}{2(-3)}=-\frac{200}{-6}=33.33[/tex]
Therefore, the price that will yield a maximum revenue is when it is $33.33.
