Solve each of these problems by computer and obtain the optimal values of the decision variables and the objective function.

a$.$ Maximize $Z=4x_1+2x_2+5x_3$

Subject to:

$1x_1+2x_2+1x_{3}25$

$1x_1+4x_2+2x_{3}40$

$3x_1+3x_2+1x_{3}30$

$x_1,x_2,x_{3}0$

b$.$ Maximize $Z=10x_1+6x_2+3x_3$

Subject to:

$1x_1+1x_2+2x_{3}25$

$2x_1+1x_2+4x_{3}40$

$1x_1+2x_2+3x_{3}40$

$x_1,x_2,x_{3}0$