Linear Programming

Solve the following Linear Programming Problems graphically: Maximise Z = 3x + 4y subject to the constraints: x + y $\leq$ 4, x $\geq$ 0, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Minimise and Maximise Z = 5x + 10y subject to x + 2y $\leq$ 120, x + y $\geq$ 60, x - 2y $\geq$ 0, x, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Maximise Z = -x + 2y, subject to the constraints: x $\geq$ 3, x + y $\geq$ 5, x + 2y $\geq$ 6, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Minimise Z = -3x + 4y subject to x + 2y $\leq$ 8, 3x + 2y $\leq$ 12, x $\geq$ 0, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Maximise Z = 5x + 3y subject to 3x + 5y $\leq$ 15, 5x + 2y $\leq$ 10, x $\geq$ 0, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Minimise Z = 3x + 5y such that x + 3y $\geq$ 3, x + y $\geq$ 2, x, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Maximise Z = 3x + 2y subject to x + 2y $\leq$ 10, 3x + y $\leq$ 15, x, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Minimise and Maximise Z = x + 2y subject to x + 2y $\geq$ 100, 2x - y $\leq$ 0, 2x + y $\leq$ 200; x, y $\geq$ 0.

Solve the following Linear Programming Problems graphically: Maximise Z = x + y, subject to x - y $\leq$ -1, -x + y $\leq$ 0, x, y $\geq$ 0.