Use the simplex or two$-$phase method to solve the following problems.

$3\mathrm{.}15$

maximize: $z=x_1+x_2$

subject $to$: $x_1+5x_{2}5$

$,2x_1+x_{2}4$

with: $x_1,x_2$ nonnegative

$3\mathrm{.}16$

maximize: $z=3x_1+4x_2$

subject $to$: $2x_1+x_{2}6$

$,2x_1+3x_{2}9$

with: $x_1,x_2$ nonnegative

$3\mathrm{.}17$

minimize: $z=x_1+2x_2$

subject $to$: $x_1+3x_{2}11$

$2x_1+x_{2}9$

with: $x_1,x_2$ nonnegative