$\approx 59$ ,$30$
Work Step by Step
From the given statement we have a contour map of $f(x,y)$ with equation of a curve $g(x,y)=8$ . Our aim is to determine the maximum and minimum values of $f(x,y)$ subject to $g(x,y)=8$ . Follow the constraint $g(x,y)=8$ which comes under nearly extreme value $60$ or, approximately to $59$ and minimum value under $30$. Hence, from the above results we can see that Maximum value is $\approx 59$ and Minimum value is $30$.