Question: A company has determined that its monthly profit (P) depends on the amount of money spent on advertising (x). The relationship is given by the equation \[P(x)=\frac{2x}{{{x}^{2}}+16}+100\], where P and x are measured in thousands of dollars.

(a) What amount should the company spend on advertising to assure maximum profit?

(b) What is the maximum profit?