I have the following $0/1$ knapsack problem \begin{aligned} &z=\max \left\{p^T x=12 x_{1}+8 x_{2}+17 x_{3}+11 x_{4}+6 x_{5}+2 x_{6}+2 x_{7}\right\} \\ &\text { s.t. } \quad a^T x=4 x_{1}+3 x_{2}+7 x_{3}+5 x_{4}+3 x_{5}+2 x_{6}+3 x_{7} \leq 9 \\ &\quad x \in\{0,1\}^{7} \end{aligned}
and I was told to give examples of a maximal feasible solution with the maximum cardinality and a maximal feasible solution with the smallest cardinality. I assume the cardinality is about the number of $x_i$ I choose to be equal to $1$, but what does the maximal refer to? Is it about having an optimal value in the objective function? If so, why not just say one of the optimal solutions instead?
"Maximal feasible" means that the solution is feasible and if you change any $x_i$ from $0$ to $1$, the solution is no longer feasible.
See section 4.3 of this paper.