IE $202$ Starting Methods Exercises

Consider the following LP:

Min $z=3x_1-x_2,+x_3$

$s.t.x_1+x_2,=-3$

$2x_1+4x_2-x_3,2$

$3x_1+2x_2,5$

$x_1$ free, $x_2,x_3,0$

Put the LP into standard form and add the necessary artificial variables for the Big $M$ method. After that, obtain the initial canonical simplex tableau.

$2.$ Consider the LP model:

Minimize $z=3x_1$

$s.t.2x_1+x_{2}6$

$3x_1+2x_2=4$

$x_1,x_{2}0$

minz$=3x_1+O{x}_2+OE$

$12x_1+x_2-51+A$

$3x_1+2x_2+A_2=4$

Solve the LP using the Big$-$M method. Does the problem have a feasible optimal solution?