Maximize $z=2x+3y$, subject to the constraints $x+y\ge 2, x+2y\ge 3, x, y\ge 0$. The feasible region is shaded in the following graph

Feasible region for an LPP is shown shaded in the figure. Maximize the objective function $z=5x+7y$

The feasible region for an $\mathrm{LPP}$ is shown shaded in the figure. Determine the maximum and minimum values of $z=x+2y$.

Determine the maximum value of $z=4x+3y$, if the feasible region for an LPP is shown shaded in the figure.