Consider the following problem.

Maximize Z $=$ x$1+4$x$2+2$x$3,$

subject to

$4$x$1+$ x$2+2$x$3<=5$

$$x$1+$ x$2+2$x$3<=10$

and

x$2>=0,$ x$3>=0$

$($no nonnegativity constraint for x$1).$

$($a$)$ Reformulate this problem so all variables have nonnegativity

constraints.

D$,$I $($b$)$ Work through the simplex method step by step to solve the

problem.

C $($c$)$ Use a software package based on the simplex method to

solve the problem.