Solve graphically the following linear programming problems:

Maximise 3x1 + 2x2 subject to:

x1 − x2 ≤ 1 x1 + x2 ≥ 3 x1, x2 ≥ 0 Step 1: Finding the vertex for each of the constraint by treating constraint of inequality nature as equality.

Constraint (I) in limiting form x1 − x2 = 1 When x1 = 0 x2 = −1 When x2 = 0 x1 = 1 Thus the vertices are (0, −1) & (1, 0)

Constraint (ii) in limiting form x1 + x2 = 3 When x1 = 0 x2 = 3 When x2 = 0 x1 = 3 Thus the vertices are (0, 3) & (3, 0).

Step 2: Plotting the co-ordinates of 1st constraint on the graph and joining them by a straight line, and shading the feasible region. Similarly drawing a straight line and shading feasible region for other constraint.