Kindly solve this plz

1- {50 points} A monopolist facm the demand function pm) for its output q but. as a bvproduct, also produces emissions {pollution} e. The monopolist's total costs of production are cm). The government enforces a tax t on each unit of emissions produced by the monopolist. a. {5 points} Write out the Lagrangian for the firm's constrained problem of choosing q and e to maximize prots subject to the constraint 3 f(q] 2 D, where f is the emissions generation function that shows hov.r much emissions result from anv given level of output. I). {15 points} Derive the first: and secondrorcler conditions and provide an economic interpretation of each of the first-order conditions. c. {15 points} Derive and sign (if possible] the comparative statics showing the effect of the per unit emissions tax on the firm's optimal level of output. d. {5 points} Derive and sign (if possible]I the comparative statics showing the effect of the per unit emissions tax on the firm's optimal level of profit. e. {10 points} Derive and sign (if possible] the comparative statics showing the effect of the per unit emissions tax on the firm's optimal price