$(30$ pts$.)$ Consider the following problem.

Maximize

s$.$t$.$

and

and

$x_1,x_2,x_{3}0$

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. $()$

c$.$ What kind of a final simplex table would indicate an infeasible solution for this problem $($in terms of basic variables$)($explain in words$)?$