Problem $2.$ Consider the following LP problem:

Maximize profit $=2x+3y$

Subject to

$2x+y8$

$-2x+y8$

$x+2y8$

$-x+2y8$

$x+y4$

$x,y0$

Con $(1)$

Con $(2)$

Con $(3)$

Con $(4)$

Con $(5)$

Con $(6)$

Q$1.$ Plot the LP$.(5$pts$)$

Q$2.$ Label all constraints, identify the feasible region, and any redundant constraints. $(5$pts$)$

Q$3.$ Find the optimal solution using the corner point method. $(5$pts$)$

Q$4.$ List the names of the binding constraints. $(3$pts$)$

Q$5.$ Plot the iso$-$profit line for profit $=12.(2pts)$