Chapter 6.1, Problem 32E

Problems 31-40 refer to the partially completed table below of the $10$ basic solutions to the e-system

$\begin{array}{l}{x}_1+x_2+s_1=24\\ 2x_1+x_2+s_2=30\\ 4x_1+x_2+s_3=48\\ \begin{array}{cccccc}& x_1& x_2& x_3& x_4& x_5\\ \left(\text{A}\right)& 0& 0& 24& 30& 48\\ \left(\text{B}\right)& 0& 24& 0& 6& 24\\ \left(\text{C}\right)& 0& 30& -6& 0& 18\\ \left(\text{D}\right)& 0& 48& -24& -18& 0\\ \left(\text{E}\right)& 24& 0& 0& -18& -48\\ \left(\text{F}\right)& 15& 0& 9& 0& -12\\ \left(\text{G}\right)& & 0& & & 0\\ \left(\text{H}\right)& & & 0& 0& \\ \left(\text{I}\right)& & & 0& & 0\\ \left(\text{J}\right)& & & & 0& 0\end{array}\end{array}$

Which of the basic solutions $\left(\text{A}\right)$ through $\left(\text{F}\right)$ are feasible? Explain.