Consider the following linear program and answer the answer the following questions.

Max$1A+2B$

$s.t.$

$1A4$

$1B3$

$2A+2B=10$

$A,B0$

$($a$)$ Show the feasible region.

$($i$)$

$($b$)$ What are the extreme points of the feasible region?

smaller $x-$value $(A,B)=(,)$

larger $x-$value $(A,B)=(,)$

$($c$)$ Find the optimal solution using the graphical procedure.

$(A,B)=(,)$