$$\left. \begin{array} { l } { \{ x , } \\ { f = 10 x + 20 y y - x ^ { 2 } - y ^ { 2 } } \\ { 2 x + 6 y = 10 } \end{array} \right.$$
$x=\frac{3\sqrt{10f-250}}{10}+5\text{, }y=-\frac{\sqrt{10f-250}}{10}$
$x=-\frac{3\sqrt{10f-250}}{10}+5\text{, }y=\frac{\sqrt{10f-250}}{10}$
$x=\frac{3\sqrt{10f-250}}{10}+5\text{, }y=-\frac{\sqrt{10f-250}}{10}$
$x=-\frac{3\sqrt{10f-250}}{10}+5\text{, }y=\frac{\sqrt{10f-250}}{10}\text{, }f\geq 25$
