Consider a price discriminating monopolist facing two markets for its good. The demand equations faced by the monopolist and its cost function are:

Market 1: Q1 = 55 - P1

Market 2: Q2 = 70 - 2P2

Cost Function: TC(Q) = 100 + 5Q, where Q = Q1 + Q2.

a.) If the monopolist can maintain the separation between the two markets, calculate the optimal output level that the firm should produce for each market to maximize profits.

b.) Determine the prices the monopoly should charge in each market, and calculate the profit of the monopoly.

c.) Construct a graph to represent your findings in items a and b.

d.) If the monopolist cannot maintain the separation between the two markets, calculate the optimal output level and determine the price will this be sold?