Exercise #$2$

The following is a dictionary $($not necessarily an optimal one$)$ from a certain optimization problem:

MAX $Z=10+3x_2-x_5$

$x_1=1+2x_2-4x_5$

$x_3=3-4x_2-3x_5$

$x_4=7,-3x_2+6x_5$

$x_{i}0$ all $i$

Explain why the dictionary must come from applying the primal simplex method, and not the dual simplex.

Identify the basic feasible solution associated.

Explain why the dictionary is not an optimal one.

Identify the entering and leaving variables.