You could use intlinprog. Assuming WNLOG that the manipulated b value is b(1),
N=numel(b);
f=[-1,zeros(1,N)].';
Aeq=[+100*f(1:N),A];
beq=[0;b(2:N)];
lb=[0;inf(N,1)];
ub=[inf;50000*ones(N,1)];
solution = intlinprog(f,1,[],[],Aeq,beq,lb,ub);
b_manipulated=100*solution(1)+100;
x=A\[b_manipulated;b(2:N)];
find(x>50000)
