$6\mathrm{.}1-3.$ For each $of$ the following linear programming models, give

your recommendation $on$ which $is$ the more efficient way $(proba-$

$bly)to$ obtain $an$ optimal solution: $by$ applying the simplex method

directly $to$ this primal problem $orby$ applying the simplex method

directly $to$ the dual problem instead. Explain.

$(a)$

Maximize $Z=10x_1-$

subject $to$

$3x_1-x_2+2x_{3}25$

$x_1-2x_2+3x_{3}25$

$5x_1+x_2+2x_{3}40$

$x_1+x_2+x_{3}90$

$2x_1-x_2+x_{3}20$

$Z=10x_1-4x_2+7x_3,$

and

$x_{1}0,x_{2}0,x_{3}0.$

$(b)$

Maximize $Z=2x_1+5x_2+3x_3+$

subject $to$

$\{\begin{array}{c}{x}_1+3x_2+2x_3+3x_4+x_{5}6\end{array}$

$4x_1+6x_2+5x_3+7x_4+x_{5}15$