Problem Set LP

$($Hint: basic solutions are solutions that satisfies $Ax=b,$ for this problem there should be $2$

basic vars and $2$ non$-$basic vars so a basic solution should consist of $2$ nonzeros and $2$

zeros values$)$

Consider the following LP

$mamize,z=2x_1+3x_2$

subject $to{x}_1+3x_{2}6$

$,3x_1+2x_{2}6$

$,x_1,x_{2}0$

$($a$)$ Express the problem as a standard LP$.$

$($b$)$ Determine all the basic solutions of the problem and classify them as feasible

or infeasible.

$($c$)$ Use direct substitution in the objective function to determine the optimal basic

feasible solution.

$($d$)$ Verify graphically that the solution in $($c$)$ is indeed optimal.

$($e$)$ Show how the infeasible basic solutions are represented on the graphical solu$-$

tion space.