Consider the following LP:

a$.$ Utilize the simplex method to solve the linear programming problem. Please demonstrate all steps clearly, including each iteration of the simplex method.

b$.$ Illustrate the feasible region graphically in the context of x$1$ and x$2.$ Highlight the path of simplex iterations by employing arrows to denote the basic feasible solutions identified at each stage of the simplex method. Additionally, label the optimal solution for clarity.

ALSO!

$1.$ Display the simplex tableau at each iteration.

$2.$ Clearly state the current basic feasible solution and specify the sets of basic and nonbasic variables.

$3.$ Report the results of the ratio test.

$4.$ Identify the entering variable and the leaving variable straightforwardly for each iteration.