(Solved): he profit generated by an information technology consulting firm can be modeled as P(x,y)=2x2+48 ...

he profit generated by an information technology consulting firm can be modeled as $P(x,y)=-2x^2+48x+216y-9y^2\text{ millon dollars }$ here $x$ thousand hours are logged by on-site desktop engineers and $y$ thousand hours are logged by network systems engineers. (a) Calculate the point of maximized profit. $x=$ $x$ thousand hours $y=$ $x$ thousand hours (b) Verify that the result of part (a) is a maximum point. Find the second partials. $\begin{array}{ll}{P}_{xx}=& ,P_{yy}=\\ P_{xy}=& ,P_{yx}=\end{array}$ Using the Determinant Test, $D(x,y)=$ . Since $D$ 0 and $P_{xx}$ 0 , the critical point is a relative maximum.