Numericals on Graphical Method of Linear Programming

(Graphical Method)

1.        Solve the following linear programming problem graphically and interpret the result.
Maximise     Z =   8x₁ + 16x₂

             Subject to            x₁ + x₂ \< 200;       x₂ \< 125
3x₁ + 6x₂ \<900

x₁, x₂  >/ 0

2.        Maximise    Z =  20x₁ + 30x₂

            Subject to             2x₁ + x₂ \< 40
4x₁ – x₂  \< 20
x_{1    >/} 30
x₁,x₂  >/ 0

3.        Solve graphically :

Minimize     Z =    0.6x₁ + x₂

            Subject to             10x₁ + 4x₂ >/20
5x₁ + 5x₂  >/ 20
2x₁ + 6x₂  >/ 12
x₁, x₂  >/ 0