Problem 5. Suppose at the beginning of the 2nd iteration of the simplex method (applied to a certain minimization problem), we have the following table
\begin{array}{rcl}
z &=& 18 - x_3 \\x_1 &=& 1 - \frac{2}{3}x_2 + \frac{1}{3}x_3 \\x_2 &=& 3 - x_2 \\x_1 &=& 1 + \frac{5}{3}x_2 - \frac{1}{3}x_3 \\x_4 &=& 3 - \frac{5}{3}x_2 + \frac{1}{3}x_3 \end{array}
(1) What are the basic variables and non-basic variables at the beginning of this iteration? What is the corresponding candidate solution to this selection of basic and non-basic variables?
(2) Finish this particular iteration of the simplex method. That is, please give the table at the beginning of the next iteration.
Problem 6. Solve the following LP using simplex method:
\begin{align*} \max_{x_1, x_2, x_3} &2x_1 + x_2 \\ \text{such that} &x_1 + x_2 = 1 \\ &x_2 + x_3 = 1 \\ &x_1, x_2, x_3 \ge 0 \end{align*}
