Problem $1$: Sensitivity AnalysisA multiple linear regression model with $10$ regressor variables was developed using $36$ observations, which

gave $S{S}_{\text{E}\text{r}\text{r}\text{o}\text{r}}=142.$ When the model is reduced by removing $4$ variables $($out of the $10$ regressor variables$),$ the

value of $S{S}_{\text{E}\text{r}\text{r}\text{o}\text{r}}$ increased to $166.$ Therefore, the $C_p$ value for the reduced model will be equal to:

$15\mathrm{.}23$

$11\mathrm{.}90$

$-0\mathrm{.}61$

$7\mathrm{.}23$

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 $3.$

Max $z=x_1+x_2$

subject to the constraints:

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

$2x_1+6x_{2}6$

$4x_1+2x_{2}8$

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

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