Convert the following Linear Programming problem into standard form.

Then find the number $of$ basic solutions and solve all the basic solutions

using the Gauss$-$Jordan elimination method. Compare basic solutions $in$

objective function and find the global maximum one. Explain all your

steps and solution $in$ detail. $(35pts.)$

Maximize $z=x+2y$

Subject $to3x+4y12$

$x+3y3$

$x0,yis$ unrestricted $in$ sign.

$In$ the Matlab environment, create a graphical representation $of$ the

problem solved $in$ Question $1to$ verify your result. $(Drawat$ least $3$

contour lines and mark your optimum solution and feasible region $on$

graph$).$ Explain your solution. $(25pts.)$