Maximize $12$

z $2$x $3$x

Subject to the constraints:

$,0.$

$326,$

$36,$

$12$

$12$

$12$

$$

$$

$$

x x

x x

x x

i$)$ Express the problem in equation form.

ii$)$ Determine all the basic solutions and classify them as feasible and infeasible.

iii$)$ Use direct substitution in the objective function to determine the optimum basic

feasible solution.

iv$)$ Verify graphically that the solution obtained in $($iii$)$ is the optimum and conclude that

the optimum solution can be determined algebraically by considering the basic feasible

solutions only.

Show how the infeasible basic solutions are represented on the graphical solution

space.