Use the complementary slackness to show that $x_1^{**}=x_3^{**}=0\mathrm{.}5,x_2^{**}=x_4^{**}=0,x_5^{**}=2$ is an optimal

solution for the following Linear Program:

max,$3\mathrm{.}1x_1+10x_2+8x_3-45\mathrm{.}2x_4+18x_5$

$s.t.x_1+x_2+x_3-x_4+2x_{5}5$

$,2x_1-4x_2+1\mathrm{.}2x_3+2x_4+7x_{5}16$

$,x_1+x_2-3x_3-x_4-10x_5-20$

$,3x_1+x_2+3x_3+\frac{3}{2}{x}_4+\frac{7}{3}{x}_{5}10$

$,x_2+x_3+6x_4+2x_{5}4\mathrm{.}5$

$,2x_2-x_4+x_{5}2$

$,x_1,x_2,x_3,x_4,x_{5}0$