In Exercises $1-4,$ write the simplex tableau for the given linear pro$-$

gramming problem. You do not need to solve the problem. $($In each

case the objective function is to be maximized.$)$

Objective function:

$z=x_1+2x_2$

Constraints:

$2x_1+x_{2}8$

$x_1+x_{2}5$

$x_1,x_{2}0$

Objective function:

$z=2x_1+3x_2+4x_3$

Constraints:

$x_1+2x_{2}12$

$x_1+x_{3}8$

$x_1,x_2,x_{3}0$

Objective function:

$z=x_1+3x_2$

Constraints:

$x_1+x_{2}4$

$x_1-x_{2}1$

$x_1,x_{2}0$

Objective function:

$z=6x_1-9x_2$

Constraints:

$2x_1-3x_{2}6$

$x_1+x_{2}20$

$x_1{x}_2=0$