3. A monopolist sells output in two markets, North and South, and the monopolist is able to charge different prioes to consumers depending on where they live. Demand in the North is given bv {1" = 12D - PH. Demand in the South if given bv {15 = ED P5. The monopolist's cost function is given by Clms } = {OH + 05W?- 3a.Suppose the monopolist can charge different prices in the North and South. 1iiil'rite down the problem that the monopolist solves to maximize prot. 3b.lf the monopolist can charge different prices in the North and South, what prices maximize its profit? 3c.Suppose the monopolist can NOT charge different prices in the North and South. Write down the problem that the monopolist solves to maximize prot. 3d.lf the monopolist can NOT charge different prices in the North and South, what price maximizes its prot