Chapter 6.3, Problem 44E

In Problem 43 and 44,

(A) Form an equivalent minimization problem with $\ge$ problem constraints (multiply inequalities by $-1$ if necessary),

(B) Form the dual of the equivalent problem.

(C) Is the dual problem a standard maximization problem in standard form? Explain.

$\begin{array}{l}\text{Minimize }C=25x_1+30x_2+50x_3\\ \text{subject to }-x_1+3x_2-8x_3\le 12\\ 6x_1-4x_2+5x_3\le 20\\ x_1,x_2,x_3\ge 0\end{array}$