$3.$ A monopolist has two geographically segmented markets. The demand curves for these market segments are:$91=500-3$p$192=800-4$p$2$where qi and pi$,$ i $=1,2,$ are the outputs and prices for segments $1$ and $2$ respectively. Suppose thefirm has a constant marginal cost for each segment of $50$ per unit and no fixed costs.a$)$ What are the profit$-$maximising prices and outputs in the two market segments, and hence the firm's profits?$(13$ marks$)$b$)$ If the monopolist is forced by regulators to charge the same price in both market segments, what is the profit$-$maximising price and the firm's profit level?$(10$ marks$)$c$)$ Tabulate the welfare of consumers in the two market segments and for the monopolist.Hence, describe who is better off and who is worse off under uniform pricing.