Provide an appropriate response.

Solve the following linear programming problem using the simplex method:

Maximize $P=5x_1+3x_2$

subject $to$

$2x_1+4x_{2}13$

$x_1+2x_{2}6$

$x_1,x_{2}0$

$2x_1+4x_{2}13$

$x_1+2x_{2}6$

$x_1,x_{2}0$

$$ MaxP$=30$ when $x_1=6,x_2=0$

Max $P=32\mathrm{.}5$ when $x_1=6\mathrm{.}5,x_2=0$

MaxP$=18$ when $x_1=0,x_2=6$

Maxi $P=9$ when $x_1=0,x_2=3$