A$5-2.$ Two$-$phase simplex $($HandWriwritten Solution please$)$

Solve the following LPs using two$-$phase simplex method. Show the steps in deriving the auxiliary LP$.$ For each phase, write down the canonical form of the LP that you are solving $($no details needed$),$ and then write down the final canonical form $($no need to show intermediate steps, though you should still use Bland's rule when solving$).$ You may use computational tools.

If you find that the original LP is infeasible, then give a mathematical reason why it is infeasible based on the final canonical form. If you find that the original LP has an optimal solution, then write down an optimal solution and its optimal value. If you find that the original LP is unbounded, then derive a series of feasible solutions whose objective values approach infinity.

$($a$)$

max,$([-3,-7,7,-1,-13)x]$

$($b$)$

max,$([-3,-7,7,-1,-13)x]$