Problem $1$: Sensitivity Analysis

For the following optimization problem, find the following:

$1.$ The optimal iteration.

$2.$ Graphically, show the possible ranges of the right hand side of the second constraint that will keep the solution feasible.

$3.$ 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 $3.$

Max z $=$ x$1+$ x$2$

subject to the constraints:

x$1$

$+$

$8$ x$2$

$<=$

$6$

$2$ x$1$

$+$

$6$ x$2$

$<=$

$6$

$4$ x$1$

$+$

$2$ x$2$

$<=$

$8$

x$1>=0$ x$2>=0$

$$ Put your solution in a pdf format.

$$ Nicely designed cover page is important.

$$ Neatness of the solution matters in grading.

$$ No hand written reports is allowed.

$$ Copying any parts of the assignment will result in a $$zero$$ in the assignment in addition to the follow up of the legal consequences according to the university bylaws.