Chapter 6.4, Problem 4E

In Problems 1-8,

(A) Introduce slack, surplus, and artificial variables and form the modified problem.

(B) Write the preliminary simplex tableau for the modified problem and the initial simplex tableau.

(C) Find the optimal solution of the modified problem by applying the simplex method to the initial simplex tableau.

(D) Find the optimal solution of the original problem, if it exists.

$\begin{array}{l}\text{Maximize }P=4x_1+3x_2\\ \text{subject to }{x}_1+3x_2\le 24\\ x_1+x_2=12\\ x_1,x_2\ge 0\end{array}$