Consider the following LP: \begin{align*} \max 8x_1 + 14x_2 + 12x_3 + 50x_4\\ \text{s. t. } x_1 + 2x_2 + 2x_3 + 16x_4 &\le 8\\ 2x_1 + 3x_2 + 4x_3 + 5x_4 &\le 15\\ 5x_1 + 6x_2 + 8x_3 + 10x_4 &\le 40\\ x_1, x_2, x_3, x_4 &\ge 0 \end{align*}
a) Is the solution $(x_1, x_2, x_3, x_4) = (1,3,0,0)$ feasible? basic?
b) Is the solution $(x_1, x_2, x_3, x_4) = (8,0,0,0)$ feasible? basic? degenerate?
So far, I have: (a) The solution is feasible because it satisfies all the three constraints. (b) The solution is not feasible because it does not satisfy the second constraint.
How do you know if the solutions are basic and degenerate?