Mathematica analitik olarak olarak buluyor sonucu
{max deger=83−11√101262,x=77+5√101262,y=29(√10−1)}



f[x_, y_] :=
Min[x (1 - y), -1 + 2 y + (4 y^2)/(4 (1 + y)), (1 - 11 x)/5]
Maximize[{f[x, y], 0 < x < 1/11, (2 (Sqrt[10] - 1))/9 < y < 1}, {x,
y}] // FullSimplify
NMaximize[{f[x, y], 0 < x < 1/11, (2 (Sqrt[10] - 1))/9 < y < 1}, {x,
y}] // N
Show[Plot3D[f[x, y], {x, 0, 1/11}, {y, (2 (Sqrt[10] - 1))/9, 1},
PlotPoints -> 100, Mesh -> None],
Graphics3D[{Red, AbsolutePointSize@6,
Point[{(77 + 5 Sqrt[10])/1262, (2 (Sqrt[10] - 1))/9, (
83 - 11 Sqrt[10])/1262}]}]]
ContourPlot[f[x, y], {x, 0, 1/11}, {y, (2 (Sqrt[10] - 1))/9, 1},
PlotLegends -> Automatic,
Epilog -> {Red, AbsolutePointSize@5,
Point[{(77 + 5 Sqrt[10])/1262, (2 (Sqrt[10] - 1))/9}]},
PlotPoints -> 100]