problem of Mathematical Application of Economics. I have attached the question 3 in the comments too. i don't think it is necessary to look at it though.

4. (25 points) Now suppose that the firm in Question 3 above is a monopolist that faces a linear demand function P = a - bQ and has total costs TC = CQ + f. Its emissions are given by the function E = a) (10 points) Derive the first- and second-order conditions. b) (10 points) Solve for the optimal levels of output and pollution control. c) (5 points) Find the effects (and their signs if possible) of changes in t and a on the optimal levels of output and pollution control