The maximum value of the objective function $$z=2 x+3 y$$ subject to the constraints $$x+y \leq 5,2 x+y \geq 4$$ and $$x \geq 0, y \geq 0$$ is

The common region of the solution of the inequations $$x+y \geq 5, y \leq 4, x \geq 2, x, y \geq 0$$ is

The maximum value of $$z=10 x+25 y$$ subject to $$0 \leq x \leq 3,0 \leq y \leq 3, x+y \leq 5$$ occurs at the point.

The objective function $$z=4 x+5 y$$ subjective to $$2 x+y \geq 7 ; 2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0$$ has minimum value at the point.