A machine consists of two independent components, the ith of which operates for exponential time with rate i . The machine works as long

A machine consists of two independent components, the ith of which operates for exponential time with rate λ i . The machine works as long as at least one of these components works. (That is, it fails when both components fail.) When one machine fails, a new machine is put into operation that has both components working. A cost K is incurred each time a machine failure occurs; Operating costs are incurred at the rate of c i per unit of time whenever the machine in use has i work components, i = 1.2. Find the long-run average cost per unit of time.