Q$-2$:

MAXZ $=51+42$

subject to

$61+4224$

$x1+226$

$-x1+x21$

$x22$

and $x1,x20$

Solution:

Problem is

MaxZ$=5x_1+4x_2$

subject to

$6x_1+4x_{2}24$

$x_1+2x_{2}6$

$-x_1+x_{2}1$

$x_{2}2$

and $x_1,x_{2}0$;

The problem is converted to canonical form by adding slack, surplus and artificial variables as appropiate

As the constraint$-1$ is of type $\text{'}\text{'}$ we should add slack variable $S1$

As the constraint$-2$ is of type $\text{'}\text{'}$ we should add slack variable $S2$

As the constraint$-3$ is of type $\text{'}\text{'}$ we should add slack variable $S_3$

As the constraint$-4$ is of type $\text{'}\text{'}$ we should add slack variable $S4$