Solution:- Given that the total revenue function
[tex]r(x)=300x-0.2x^2[/tex] ,where x is the number of rooms filled
Now, differentiating the function w.r.t. x,we get
[tex]r'(x)=300-0.4x[/tex]
To find critical points ,Put [tex]r'(x)=0[/tex]
[tex]\Rightarrow300-0.4x=0\\\Rightarrow0.4x=300\\\Rightarrow x=750\\\text{Now}\\r"(x)=-0.4 <0\text{(by second derivate test)})\\\text{Maximum revenue will produce by filling x=750 rooms in dante's villas.}[/tex]
