Direction: Consider the linear Programme (LP)
Max 4x + 6y
Subject to
3x + 2y < 6
2x + 3y < 6
x, y > 0
-
After introducing slack variables s and t, the initial basic feasible solution is represented by the table below (basic variables are s = 6 and t = 6, and the objective function value is 0).
After some simplex iterations, the following table is obtained
From this, one can conclude that
-
- the LP has a unique optimal solution
- the LP has an optimal solution that is not unique
- the LP is infeasible
- the LP is unbounded
Correct Option: B
z = 4x + 6y
3x + 2y ≤ 6
2x + 3y ≤ 6
x, y > 0
Feasible region (O–A–B–C–0)
Since, Slope of objective function is equal to the slope of constraint Hence LPP has multiple optimal solution
At B (6/5, 6/5)
Z = 12 At C (0,2)
Z = 12
Hence solution is not unique solution.
