The maximum revenue will be at the x-coordinate of the vertex point of the equation
[tex]R(x)=100x-0.4x^2[/tex]The form of the quadratic function is
[tex]f(x)=ax^2+bx+c[/tex]Its vertex is (h, k), where
[tex]h=-\frac{b}{2a}[/tex]From the given function
[tex]\begin{gathered} a=-0.4 \\ b=100 \end{gathered}[/tex]Substitute them to find the value of h
[tex]\begin{gathered} h=-\frac{100}{-0.4} \\ h=250 \end{gathered}[/tex]Then the x-coordinate of the maximum point of the function is 250
The number of rooms rented which produces the maximum revenue is 250 rooms
The answer is 250
