can you slove this questions $($For$)))$For the following LP problem:

maxZ$=-x_1+5x_2$

$s.t{x}_1+2x_{2}0\mathrm{.}5$

$-x_1+3x_{2}0\mathrm{.}5$

$x_1,x_{2}0$

a$)$ Write the dual of the given problem $.$

minW$=0\mathrm{.}5y_1+0\mathrm{.}5y_2$

$s.t{y}_1-y_2-1$

$2y_1+3y_{2}5$

$y_1,y_{2}0$

a$)$ Row zero of the optimal simplex tableau of the given problem is given below.

Calculate optimal objective function value $Z.$ Row $0$:$Z+0\mathrm{.}4S_1+1\mathrm{.}4S_2=?$

$Z=W=0\mathrm{.}50\mathrm{.}4+0\mathrm{.}51\mathrm{.}4=0\mathrm{.}9$