Consider the following algebraic form of a linear programming model where $x_1,x_2,x_3,$ and $x_4$ are

the decision variables and $Z$ is the value of the objective function.

Maximize $Z=50x_1+60x_2+40x_3+30x_4,$

subject $to$

$3x_1+5x_2+2x_3+3x_{4}130$

$4x_1+3x_2+5x_3+x_{4}130$

$2x_1+6x_2+4x_3+7x_{4}190$

and

$x_{1}0,x_{2}0,x_{3}0,x_{4}0.$

a$.$ Use Solver $($which applies the simplex method$)$ to solve the model.

b$.$ Examine the results of applying the interior$-$point algorithm