The maximum value of $$Z=12 x+13 y$$, subject to constraints $$x \geq 0, y \geq 0, x+y \leq 5$$ and $$3 x+y \leq 9$$ is

The minimum value of $$Z=3 x+5 y$$, given subject to the constraints $$x+y \geq 2, x+3 y \geq 3, x, y \geq 0$$ is

Shade the feasible region for the inequations $$6x+4y\le120, 3x+10y\le180,x,y\ge0$$ in a rough figure.

The maximum of Z is where, $$Z=4x+2y$$ subject to constraints $$4x+2y\ge46,x+3y\le24$$ and $$x,y\ge0$$ is