For the remainder of this problem, we're going to analyze the average cost associated with different preventa- tive maintenance policies. Doing preventative maintenance costs cm =$50, while repairing a pump that has failed costs cr = $250. We schedule preventative maintenance at time tm. We amortize the operating cost of the pump over its lifetime and define the running cost R of the pump as the cost (repair or maintenance) divided by the running time. If the pump fails prematurely (that is, if t ≤ tm) we have R = cr /t; otherwise we do preventative maintenance and the running cost is R = cm/tm