Solve the linear programming problem by the simplex method. $($There may be more than one correct answer.$)$

Maximize

P $=3$x $+3$y $+4$z

subject to

x $+$ y $+3$z

$4$x $+4$y $+3$z

x $>=0,$ y $>=0,$ z $>=0$

The maximum is P $=$ at

$($x$,$ y$,$ z$)=$Solve the linear programming problem by the simplex method. $($There may be more than one correct answer.$)$

Maximize $P=3x+3y+4z$

subject $tox+y+3z15$

$,4x+4y+3z110$

$,x0,y0,z0$

The maximum is $P=$

at $.$