A coal fired power plant is producing 3,500 MW of electricity for a nearby town. Assume that the efficiency of this power plant is 35% and the rest of the input energy goes to waste: 20% is lost to the smokestack and the remaining waste heat needs to be taken away by a cool stream that flows nearby. (a) (8 pts) Calculate the heat input rate needed for this power plant as well as the waste heat for the smokestack, and the waste heat that is being removed via colling water (all in MW). Assume the capacity factor is 100%. (b) (10 pts) If the cooling water is only allowed to rise in temperature by 15%, what flow rate of water is needed? (c) (7 pts) If waste heat is considered a pollutant (it is killing some of the fish that would otherwise thrive in the stream). Draw a figure showing the Cost vs. quantity (per person power consumption) with the marginal demand and marginal cost curves. Some states do not allow this, but explain why the town might want to impose an extra sales tax on the electricity purchased per person. Draw what this could mean on the figure and briefly explain how would this change the set-up for problem in part (a) and (b)?