Minimise $C(x,y)=11x+3y$ subject to the constraints.

Minimise $$C(x,y)=11x+3y$$ subject to the constraints $$g(x,y)=-3x^2-3y^2+10xy$$ and $$x\geq 0, y\geq 0$$. I started solving using this Lagrange multiplier, but the constraint set is not compact, right? So, how can I argue whether the critical point is a maximum or a minimum or a saddle point?