Chapter 4, Problem 27RE

Convert each problem into a maximization problem and then solve each problem using both the dual method and the method of Section 4.4.

27. $\begin{array}{ll}\text{Minimize}\hfill & w=7y_1+2y_2+3y_3\hfill \\ \text{subject}\text{to:}\hfill & y_1+y_2+2y_3\ge 48\hfill \\ \hfill & y_1+y_2\ge 12\hfill \\ \hfill & y_3\ge 10\hfill \\ \hfill & 3y_1+y_3\ge 30\hfill \\ \text{with}\hfill & y_1\ge 0,y_2\ge 0,y_3\ge 0.\hfill \end{array}$