$($a$)$

Maximize $z=3x_1-2x_2+4x_3$

subject $to{x}_1+x_2+3x_{3}10$

$x_1+2x_{3}22$

$3x_2+x_{3}13$

$x_1,x_{2}0$

$x_{3}0$

$($b$)$

Minimize $z=-2x_1+3x_2$

subject $to-x_1+2x_{2}8$

$2x_1+x_{2}12$

$x_1-x_2=9$

$x_{1}0$

$x_2$ unrestricted

Solve the primal models given in Question $3$ using Lindo. Print out two copies of the output files. Attach one of the output file to this homework, and bring the other one to the class. We will talk about dual prices, and feasibility and optimality ranges on those files.