Consider the following linear program.

max $2$x $+3$y

s$/$t x $+$ y $<=80$

x $+3$y $>=90$

x $>=0,$ y $>=0.$

$($a$)[2$ pts$]$ Identify the region where x $>=0$ and y $>=0.$

$2$

$($b$)[2$ pts$]$ Compute the point where x $+$ y $=80$ and x $+3$y $=90$ intersect.

$($c$)[2$ pts$]$ Identify the region where x $+$ y $<=80.$

$($d$)[2$ pts$]$ Identify the region where x $+3$y $>=90.$

$3$

$($e$)[2$ pts$]$ Identify the feasible region.

$($f$)[2$ pts$]$ Identify all extreme points.

$($g$)[2$ pts$]$ Find the optimal solution.