Solve the linear programming problem graphically.

Maximize $z=20x+15y$, subject to the conditions $2x+y\le 200, x+y\le 150 \text{ and }x\ge 0, y\ge 0$

Solve the linear programming problem graphically.

Maximize and minimize $z=5x+2y$, subject to the conditions. $x-2y\le 2, 3x+2y\le 12, -3x+2y\le 3 \text{ and }x\ge 0, y\ge 0$.

Solve graphically the following linear programming problem:

Maximize or minimize $Z=x+2y$ subject to constraints $x+2y\ge 100, 2x-y\le 0, 2x+y\le 200 \& x\ge 0, y\ge 0$.

Solve graphically the following linear programming problem:

Maximize or minimize $Z=1000x+600y$ subject to constraints $x+y\le 200, x\ge 20, y\ge 4x, x\ge 0 \& y\ge 0$.