27. 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.