Marathon petroleum distribution company manages 600 gas stationsin Michigan. Each gas station typically has four undergroundstorage tanks (UGST), three for gasoline and one for diesel. TheUGST develop leaks sometimes due to corrosion or changes in soilconditions. Based on historical data, Marathon estimates that theprobability that a given UGST develops a leak during a given yearis 0.002 for gasoline storage tanks and higher at 0.003 for dieselstorage tanks potentially due to higher density of diesel andhigher sulfur content. Marathon also estimates that an averageleaking tank results in $10,000 in repair costs, $5000 worth lostfuel and $50,000 in clean up costs. Further, disruption to the gasstation operations during repairs to the leaking tank, results inlost sales of $100,000 on which the gas station would have earned apretax profit of $20,000.

An insurance company offers an insurance policy that would payfor repair costs, lost fuel costs and clean up costs (but not forbusiness interruption and lost sales) in the case a UGST develops aleak. The insurance premium is $150 per UGST/year.

Alternatively, Tank Repairs Incorporated has developed a newtechnology of spray coating the insides of the UGSTs with a specialself-sealing polymer, which would reduce the probability of leakageto 0.0005 per year/tank. However, the coating has to be done everyyear when the tanks are emptied for cleaning and inspection. TankRepairs Inc. offers to coat the UGSTs managed by Marathon at therate of $140/tank. Each time a tank is coated, it results inincremental lost sales of $200 on which Marathon would have earneda profit of $40.

What should Marathon do? Show all your intermediate steps andcalculations clearly and state your assumptions.