1. Two paper manufacturers near the same river decide simultaneously and independently how much waste water to dump in the river a day. They use similar production technologies and face the same regulatory environment, and their profits are calculated by the following formula (given in thousand dollars per day): m.(z., z,) = 10 +4.8x, + 0.4mix, - z? - 2c?, for i, j = 1, 2, where i and j denote the two different manufacturers and r, ( = 1, 2) are their respective pollution levels, measured in thousand liters of waste water. a. Assuming that the objective of both manufacturers is to maximize profits, find the best- response functions. (10 pts) b. Calculate the Nash equilibrium pollution levels. (10 pts) c. Do the manufacturers benefit from polluting (as in the Nash equilibrium) or would they be better off if they didn't pollute at all? (5 pts)