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 thatConsider the linear programme (LP) Max 4x + 6y Subject to 3x + 2y $\leq$ 6 2x + 3y $\leq$ 6 x, y $\leq$ 0 The dual for the LP is

  1. $\text{min 6u+6v}\\ \text{Subject to} \\ 3u+2v\geq4 \\ 2u+3v\geq6 \\ u.v\geq0$
  2. $\text{min 6u+6v}\\ \text{Subject to} \\ 3u+2v\geq4 \\ 2u+3v\leq6 \\ u.v\geq0$
  3. $\text{min 4u+6v}\\ \text{Subject to} \\ 3u+2v\geq4 \\ 2u+3v\geq6 \\ u.v\geq0$
  4. $\text{min 4u+6v}\\ \text{Subject to} \\ 3u+2v\geq4 \\ 2u+3v\geq6 \\ u.v\geq0$
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