Question: A machine consists of two independent components, the ith of which functions for an exponential time with rate i . The machine functions as long

A machine consists of two independent components, the ith of which functions for an exponential time with rate λi . The machine functions as long as at least one of these components function. (That is, it fails when both components have failed.)

When a machine fails, a new machine having both its components working is put into use. A cost K is incurred whenever a machine failure occurs; operating costs at rate ci per unit time are incurred whenever the machine in use has i working components, i = 1, 2. Find the long-run average cost per unit time.

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