`x + 2y le 3, 3x + 4y ge 12, x ge 0, y ge 1`

Draw the graph and find the common region of the following system of incquations : x + 2y le 3 , 3x + 4y ge 12 , x ge 0 , y ge 0

Solve the following system of inequalities graphically. x - 2y le 3 , 3x + 4y ge 12 , x ge 0 , y ge 0

Z = -3x + 4y x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0

Solve the following graphically x + 4y le 8 , 3x - 4y le 12 , x ge 0 , y ge 0

Z = -3x + 4y x + 2y le 8, 3x + 2y le 12, x ge 0 , y ge 0 .

Minimize Z = -3x + 4y subject ot constraints : x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0 .

Minimise Z = -3x + 4y subject to x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0 .

Maximize Z = 3x + 4y subject to the constraints : x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0 using graph.

(a) Draw the feasible region of inequation: x + y le 4, x ge 0, y ge 0 (b) Draw the graph of the following LPP: 3x + y le 17, x, y ge 0 (c) Shade the feasible region of LLP: (i) x + 3y ge 3, x + y ge 2, x ge 0, y ge 0 (ii) x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0

3x + 2y le 12, x ge 1, y ge 2