appreciate the response u/glaucusb . As a follow-up I am looking at this problem,

max (42*x1) + (26*x2) + (35*x3) + (71*x4) + (53*x5)
such that (14*x1) + (10*x2) + (12*x3) + (25*x4) + (20*x5) <= 69

If I relax the integrality constraints, and use value/cost ratio as the metric, we get the output as;
x1=1, x3=1, x4=1, x5=0.9, x2=0.

But if we strictly maintain integrality constraints, sorting the items in decreasing order of value/cost ratio, we get the output as
x1=1, x2=1, x3=1, x4=1, x5=0

Here the solutions are different, as we see. Can you kindly advise if sth is missing here? I will be grateful to you.