$**$Question $2$ only$**($Graphic analysis$)$ Consider the following program:

Minimize: $6x_1+7x_2$

Subject to:

$4x_1+6x_{2}48$

$2x_1+2x_{2}18$

$2x_1+x_{2}16$

$x_{1}0$ and $x_{2}0$

Please delineate the feasible region, identify the optimal solution $(x_1,x_2)$ and mark it on the

graph. $($no need to solve for the value of $x_1$ and $x_2.)$

Please highlight the binding constraints at this optimal solution.$($Graphic analysis$)$ Consider the following program:

Minimize: $6x_1+7x_2$

Subject $to$:

$4x_1+6x_{2}48$

$2x_1+2x_{2}18$

$2x_1+x_{2}16$

$x_{1}0$ and $x_{2}0$

Please delineate the feasible region, identify the optimal solution $(x_1,x_2)$ and mark it on the

graph. $($no need to solve for the value of $x_1$ and $x_2.)$

Please highlight the binding constraints at this optimal solution.

$($Sensitivity analysis$)$ Continue with the problem above. Suppose we solve the problem using

the Excel Solver and create the "Sensitivity Report". In this report, we have the following

tables:

If the coefficient for $x_1$ increases to be $7\mathrm{.}1,$ which corner point is mostly likely to be the

optimal solution, and why. Please label the optimal solution as $"Z"$ and mark it on the graph.

$($independent of the preceding question$)$ If the coefficient for $x_2$ increases to be $8\mathrm{.}5,$ which

corner point is mostly likely to be the optimal solution.

Constraints

The three rows, from top down, one$-$one correspond to the three constraints in the

formulation. What if we increase the right$-$hand side of the first constraint to be $53?$ What

would be the new objective function value?