Consider the following problem: $(20)$

$1\mathrm{.}1.$ Solve this problem graphically.

$1\mathrm{.}2.$ Solve the problem by the simplex method.

MaxZ$=5x_1+4x_2$

$s.t.$

$x_1+2x_{2}6$

$-2x_1+x_{2}4$

$5x_1+3x_{2}15$

$x_1,x_{2}0$