G A coal-fired power plant produces power p with costs c(p)=\frac{p^2}{6}. Each unit of power earns the plant \$ 10. Burning coal releases particulate matter (PM2.5), a pollutant that is known to cause heart disease, lung disease, and birth defects. The coal plant borders a wildlife sanctuary which sells tourism visits t for a price $30. However, the sanctuary's animals are getting sick due to the negative externality of PM2.5, such that the costs to the sanctuary are c(t)=\frac{t^2}{6} + \frac{p^2}{6}. The local government decides to tax the coal plant to internalize its negative externality. What tax will restore the social optimum?