In a certain country the government charges tax on each litre of petrol sold to motorists. The revenue per year is \(R\) million dollars when the rate of tax is \(x\) dollars per litre. The variation of \(R\) with \(x\) is modelled by the differential equation

\(\frac{dR}{dx} = R \left( \frac{1}{x} - 0.57 \right),\)

where \(R\) and \(x\) are taken to be continuous variables. When \(x = 0.5, R = 16.8\).

(i) Solve the differential equation and obtain an expression for \(R\) in terms of \(x\). [6]

(ii) This model predicts that \(R\) cannot exceed a certain amount. Find this maximum value of \(R\). [3]