Multiple choice

Consider the linear programme (LP) Max 4x + 6y Subject to 3x + 2y $\leq$ 6 2x + 3y $\leq$ 6 x, y $\leq$ 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. ||||||| |---|---|---|---|---|---| | | -4 | -6 | 0 | 0 | 0 | | s | 3 | 2 | 1 | 0 | 6 | | t | 2 | 3 | 0 | 1 | 6 | | | x | y | s | t | RHS |

After some simplex iterations, the following table is obtained ||||||| |---|---|---|---|---|---| | | 0 | 0 | 0 | 2 | 12 | | s | 5/3 | 0 | 1 | -1/3 | 2 | | y | 2/3 | 1 | 0 | 1/3 | 2 | | | x | y | s | t | RHS |

From this, one can conclude that

  1. The LP has unique optimal solution.

  2. The LP has an optimal solution that is not unique.

  3. The LP is infeasible.

  4. The LP is unbounded.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\text{The LP has an optimal solution that is not unique, because zero has appeared in}$ $\text{the non-basic variable (x and y) column, in optimal solution}$

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