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

MAX Z $=10+3$x$2$ x$5$

x$1=1+2$x$24$ x$5$

x$3=34$x$23$ x$5$

x$4=73$x$2+6$ x$5$

xi $>=0$ all i

$1.$ Explain why the dictionary must come from applying the primal simplex method, and not the dual simplex.

$2.$ Identify the basic feasible solution associated.

$3.$ Explain why the dictionary is not an optimal one.

$4.$ Identify the entering and leaving variables.