Could someone please explain if it has been proven that the following problem is NP-hard $$\mathrm{maximize}\sum x_i$$ $$A\mathbf x\leq1$$
$$x_i\in\{0,1\}\forall i$$ where $\mathbf x = (x_1,\dots,x_N)^T$, $A$ is a constant matrix and $x_i$ are binary variables.
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