A manufacturing company determines its total production cost based on machine operating hours using a composite function. The number of kilograms of raw material required is given by \(g(x) = 3x + 2\), where \(x\) represents the machine operating hours. The cost per kilogram of raw material is modeled by \(f(x) = 5x + 10\). The composite function \(C(x) = f(g(x))\) thus becomes \(C(x) = 15x + 20\), which gives the total production cost (in dollars) for \(x\) operating hours.

(a) Calculate the total production cost when the machine operates for 4 hours.
(b) Find the inverse function \(C^{-1}(y)\) that determines the operating hours required for a given production cost \(y\).