How do I maximize the function $f(x,y)=g(x,y)-ax-by$ given non-negativity and inequality constraints in the description?

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If

$$f(x,y)=g(x,y)-ax-by,$$ $$x,y,a,b \ge 0,$$ $$ax+by\le m$$ and $$\frac {\partial g(x,y)}{\partial x}\gt 0$$ $$\frac {\partial g(x,y)}{\partial y}\gt0$$ $$\frac {\partial ^2g(x,y)}{\partial x^2}\lt 0$$ $$\frac {\partial ^2g(x,y)}{\partial y^2} \lt 0$$

For what values of $x,y$ (preferably as an expression of a,b, and m, or as a differential equation), is the value of $f$ maximum? What is the maximum value?