Assume you are the President of British Petroleum (BP). You note that the Exxon Valdez spill cost Exxon Corp, approximately \(\$ 8\) billion. You are trying to decide on the thickness of the hull of your new supertanker. Your engineers tell you that the probability of an accident ever occurring ( \(p\) ) is inversely proportional to hull thickness: \(p t=0.002\) where \(t\) is the hull thickness in centimeters. But the costs of a thicker hull rise rapidly as the thickness rises. Costs (in million \$) are given by \(C(t)=t^{2}\) where \(t\) is the thickness in centimeters. Assume an accident's damage is the same as with Exxon. What is the socially desirable hull thickness? If there is a probability of \(10 \%\) that BP will not be found liable in case of an accident, what will BP choose as a hull thickness (ignoring the fact that BP may be socially responsible and take the socially desirable route)? (Hint: Use calculus or graphs and pay attention to units.)