A monopolist sells a product in three countries. The demand Q as a function of price P in each country is Q1 = 45 - 1/2 p₁, Q2 = 50 - 1/3 p₂, and Q3 = 75 -1/4 p₃. Suppose the total cost for the monopolist is TC = 30 +(Q₁ + Q₂ + Q₃)^2. If the monopolist's profit function is =TR - TC where TR = P₁Q₁ + P₂Q₂ + P₃Q₃ then find the profit maximizing demand and the associated total revenue.