Use the two$-$phase simplex method to minimize

subject to

If there are no solutions, enter None for

$.$

For the minimum value, enter the values of

$,$

$,$ and

in the spaces provided. If there are no solutions, you may leave these answers blank.

caution: there can be alternate optimal solutions but unfortunately only one is being graded as correct. If you get the correct value for z and one of the variables, then try looking at your optimal tableau and see if one of the NBV

$\text{'}$s or

$\text{'}$s has a $0$ in row$0($maybe more than one$)$ and pivot on the one that will become a basic variable while leaving alone your basic variables from