Chapter 6.3, Problem 12E

In Problems 11 and 12, a minimization problem, the corresponding dual problem, and the final simplex tableau in the solution of the dual problem are given.

(A) Find the optimal solution of the dual problem.

(B) Find the optimal solution of the minimization problem.

$\begin{array}{l}\text{Minimize }C=16x_1+25x_2\\ \text{subject to }3x_1+5x_2\ge 30\\ \text{ 2}{x}_1+3x_2\ge 19\\ x_1,x_2\ge 0\\ \text{Maximize }P=30y_1+19y_2\\ \text{subject to }3y_1+2y_2\le 16\\ 5y_1+3y_2\le 25\\ y_1,y_2\ge 0\\ y_1{y}_2{x}_1{x}_{2}P\\ \left[\begin{array}{cccccc}0& 1& 5& -3& 0& 5\\ 1& 0& -3& 2& 0& 2\\ 0& 0& 5& 3& 1& 155\end{array}\right]\end{array}$