Chapter 6.3, Problem 43E

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.

$\begin{array}{l}\text{Minimize }C=3x_1+x_2+5x_3\\ \text{subject to }2x_1-6x_2-x_3\le 10\\ -5x_1+x_2+4x_3\ge 15\\ x_1,x_2,x_3\ge 0\end{array}$