$5\mathrm{.}25.$ You are given the following linear programming model in algebraic form, with $x_1$ and $x_2$ as the

decision variables:

Minimize $,$ Cost $=40x_1+50x_2$

subject to

Constraint $1$:$2x_1+3x_{2}30$

Constraint $2$ : $x_1+x_{2}12$

Constraint $3$ : $2x_1+x_{2}20$

and

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

a$.$ Use the graphical method to solve this model.

b$.$ How does the optimal solution change if the objective function is changed to Cost $=40x_1+70x_2?$

c$.$ How does the optimal solution change if the third functional constraint is changed to

$2x_1+x_{2}15?$

d$.$ Now incorporate the original model into a spreadsheet and use Solver to solve this model.

$c.$ Use Excel to do parts $b$ and $c.$