Question $2(3$ marks$)$:

Consider the following linear program:

Minimize Z$=8$x$\_(1)+2$x$\_(2)$

Subject to: $2$x$\_(1)-6$x

$,5$x$\_(1)+4$x$\_(2)>=40$

$,$x$\_(1)+2$x$\_(2)>=12$

$,$x

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

find the optimal solution using the graphical method. What is the value of the objective function

at the optimal solution? Write your answers into the following table.

You must insert an image of your graph below to support your answers.