Consider the following model:

Max$4x_1+x_2$

$x_1+2x_2=6$

$x_1-x_{2}3$

$2x_1+x_{2}10$

$x_{1}0,x_{2}0$

$($a$)$ draw the model in $2-$dimensional space $($with hands$-$on paper$)$ and show the feasible solution area $(10$ points$)$

$($b$)$ solve the model using the Simplex algorithm $($Big M method$)(20$ points$)$

$($c$)$ State the corresponding dual model $(10$ points$)$