A monopolist produces a product in one central production facility using the cost structure: TC = (1/2) Q2 +300 and sells it in two different markets with the following demand functions:
Market 1: P1 = 60 - (1/4)Q1
Market 2: P2 = 80 - (1/2)Q2
where Q =Q1 + Q2
Calculate the amounts of outputs, Q1 and Q2 that the monopolist should produce and the prices that it should charge if it wants to maximize total profit. Calculate the amount of total profit.