Solve the following problem using graphical linear programming and then answer the following question.

Minimize $Z=2x+3y$

subject to:

$4x+2y20$

$2x+6y18$

$x+2y12$

$x,y0$

What are the optimal values of the decision variables and $Z?$

Solve the following problem using Excel Solver and obtain the optimal values for the decision variables and objective function.

Maximize $Z=10x+6y+3z$

subject to:

$x+y+2z25$

$2x+y+4z40$

$x+2y+3z40$

$x,y,z0$

What are the optimal values of the decision variables and $Z?$