Question $3(7$ marks$)$:

Use the simplex method to solve the following linear program:

Minimize Z$-2$x$\_(1)+2$x$\_(2)$

Subject to:

x$\_(1)+3$x

$3$x$\_(1)+$x$\_(2)>=13$

x$\_(1)-$x$\_(2)=3$

x$\_(1),$x$\_(2)>=0$

What are the optimal values of basic variables $($RHS$)$ and non$-$basic variables and the objective

function $($Z$)$ in the final simplex table? Wribe your answers into the following table $(7$ marks$)$:

You must complete the following simplex tables to support your answers.