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?

1. alwaysrain irrigation, inc. would like to determine capacity requirements for the next four years. currently, two production lines are in place for making bronze and plastic sprinklers. three types of sprinklers are available in both bronze and plastic: 90-degree nozzle sprinklers, 180-degree nozzle sprinklers, and 360-degree nozzle sprinklers. management has forecast demand for the next four years as follows: both production lines can produce all the different types of nozzles. the bronze machines needed for the bronze sprinklers require two operators and can produce up to 12,000 sprinklers. the plastic injection molding machine needed for the plastic sprinklers requires four operators and can produce up to 200,000 sprinklers. three bronze machines and only one injection molding machine are available. what are the capacity requirements for the next four years? (assume that there is no learning.)