Solve with graphical method a) Min F=x^2 + y^2 S.t x+y≤10 x+y≥5 2x+y≤15 x,y≥0 b) "Optimum point of a linear programming problem always lies on one of the corner points of the graph’s feasible region"...

  S.t     x+y≤10
            x+y≥5
            2x+y≤15
            x,y≥0

b) "Optimum point of a linear programming problem always lies on one of the corner points of the graph’s feasible region" Does this also apply to nonlinear programming ?
If not Explain how to get a nonlinear programming answer (max , min) from a graph.