We are given positive values $b_1, b_2,\dots,b_n$ and we need to find if there exist $n$ positive numbers $x_1, x_2, x_3,\dots,x_n$ such that if
$$x_1+x_2+\cdots+x_n =: S$$
$$S\leq b_1 x_1$$
$$S\leq b_2 x_2$$
$$S\leq b_n x_n$$
Is there mathematical solution to this problem or some direct formula? We just need to state if sum can satisfy all inequalities or not .