$,)$ Consider the following problem.

Maximize

s$.$t$.$

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

$x_1+x_2+2x_{3}20$

$3x_1+6x_2-5x_3=50$

$x_1+3x_2+5x_{3}30$

and

$x_1+3x_2+5x_{3}30$

$x_1,x_2,x_{3}0$

a$.$ Reformulate this problem to fit our standard form $($canonical form$)$ for a linear programming model.

b$.$ Using the Big $M$ method, $1.$ Construct the complete first simplex table for the simplex method, $2.$Identify the corresponding initial BF solution, $3.$Identify the initial entering basic variable and the leaving basic variable. $()$ terms of basic variables$)($explain in words$)?$