Problem $1$: Sensitivity Analysis

For the following optimization problem, find the following:

The optimal iteration.

Graphically, show the possible ranges of the right hand side of the

second constraint that will keep the solution feasible.

Analytically $-$using the optimal iteration$-$show the feasible ranges of

the increments in the RHS of the second constraint that will keep the

solution feasible.

Hint: your answers in part $2$ should match with part $3.$

Maxz$=x_1+x_2$

subject to the constraints:

$\{\begin{array}{c}{x}_1+8x_{2}6\end{array}$

$2x_1+6x_{2}6$

$4x_1+2x_{2}8$

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