Solve the following Linear Programming Problems graphically:

1. Maximise Z=3x+4y
subject to the constraints : x+y≤4, x≥0, y≥0.

2. Minimise Z=–3x+4y
subject to x+2y≤8, 3x+2y≤12, x≥0, y≥0.

3. Maximise Z=5x+3y
subject to 3x+5y≤15, 5x+2y≤10, x≥0, y≥0.

4. Minimise Z=3x+5y
such that x+3y≥3, x+y≥2, x,y≥0.

5. Maximise Z=3x+2y
subject to x+2y≤10, 3x+y≤15, x,y≥0.

6. Minimise Z=x+2y
subject to 2x+y≥3, x+2y≥6, x,y≥0.

Show that the minimum of Z occurs at more than two points.

7. Minimise and Maximise Z=5x+10y
subject to x+2y≤120, x+y≥60, x–2y≥0, x,y≥0.

8. Minimise and Maximise Z=x+2y
subject to x+2y≥100, 2x–y≤0, 2x+y≤200, x,y≥0.

9. Maximise Z=–x+2y subject to the constraints:
x≥3, x+y≥5, x+2y≥6, y≥0.

10. Maximise Z=x+y, subject to x–y≤–1, –x+y≤0, x,y≥0.