Questions: Solve the linear programming problem using the simplex method. Maximize P = -x1 + 2x2 subject to -x1 + x2 ≤ 2 -x1 + 3x2 ≤ 12 x1 - 4x2 ≤ 6 x1, x2 ≥ 0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of P is P= when x1= and x2= . (Simplify your answers.) B. There is no optimal solution.

c = [-1, 2] A = [[-1, 1], [-1, 3], [1, -4]] b = [2, 12, 6]

Introduce slack variables to convert inequalities to equalities. The initial tableau is formed. $$ \begin{array}{c} -1 & 1 & 1 & 0 & 0 & 2 \\ -1 & 3 & 0 & 1 & 0 & 12 \\ 1 & -4 & 0 & 0 & 1 & 6 \\ \hline -1 & 2 & 0 & 0 & 0 & 0 \\ \end{array} $$

Perform row operations to make all other entries in column zero and pivot entry one. $$ \begin{array}{c} 0 & -3 & 1 & 0 & 1 & 8 \\ 0 & -1 & 0 & 1 & 1 & 18 \\ 1 & -4 & 0 & 0 & 1 & 6 \\ \hline 0 & -2 & 0 & 0 & 1 & 6 \\ \end{array} $$

Perform row operations to make all other entries in column zero and pivot entry one. $$ \begin{array}{c} & 1 & -0.33 & & -0.33 & -2.67 \\ 0 & 0 & -0.33 & 1 & 0.67 & 15.33 \\ 1 & 0 & -1.33 & 0 & -0.33 & -4.67 \\ \hline 0 & 0 & -0.67 & 0 & 0.33 & 0.67 \\ \end{array} $$

Perform row operations to make all other entries in column zero and pivot entry one. $$ \begin{array}{c}