Consider the following linear program.

max z $=3$x$1+4$x$2+$ x$3+2$x$4+3$x$5$

s$.$t$.$ x$1+$ x$2+$ x$3$ x$4+2$x$5<=12$

x$12$x$2$ x$3$ x$4$ x$5>=30$

x$1,$ x$2,$ x$3,$ x$4,$ x$5>=0$

$($a$)$ Transform the problem into standard form.

$($b$)$ Use the simplex method to solve the problem.