A manufacturer studies how the ratio of maintenance cost to production cost (in suitable monetary units) varies with the daily production level x (in units). The ratio is modelled by
R(x)=5x3−7x+2003x2+100x+400,x>0.
(a) Calculate x→∞limR(x).
(b) Interpret the value obtained in part (a) in the given context. State, in one short sentence, what the company can expect for very large production levels.