Problem

Consider the following Linear Program:

MINIMIZE $Z=3x_1+5x_2+4x_3$

subject to

$-x_1+3x_2+5x_{3}30(Constraint-A)$

$5x_1+6x_2+5x_{3}20,($ Constraint$-B)$

$2x_1+x_2+2x_{3}10(Constraint-C)$

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

a$)$ Work through Simplex, using the $B$ ig $M$ method, to determine the Optimal solution.