Suppose a natural gas plant is deciding how much to contribute toward emissions reductions by installing scrubbers on their smokestacks. The following function represents their utility from contributing toward pollution control: U1 = 20 c1 + 0.4(c1 + c2) (a) Maximize the given utility function with respect to c1 (b) What does a negative derivative tell us about the natural gas plant's willingness to contribute toward emissions reductions? (c) How would their response change if the alpha variable (0.4) were greater than 1?