solution.

$($b$)$ Use simplex method, solve the following linear programming problem:

Max. $Z=3x_1+2x_2$ subject to $x_1+2x_{2}6,2x_1+x_{2}6,$ and $x_1,x_{2}0.$

Append an additional constraint $x_1+x_{2}3$ in the optimal simplex tableau. Does the original optimal

solution remain optimal? if an additional variable $x_3$ with activity vector $a^{(3)}=[1,1{]}^T$ and price $c_3=2$

is introduced in the original problem then update the original optimal simplex tableau and find its

optimal solution.

$(4,10)$