Firm 'Y' operates in a perfectly competitive market where demand is given by P=13-0.03qd and supply is given by P=9+0.05qs. 

a) Considering a cost function of C(Q)=140+Q+0.3Q2, calculate the optimal production quantity that maximizes Y's profits. Include the calculations in your answer. (12 points)

b) Let us assume that Y is the monopolist in the market. considering the same demand and cost function as in the first part of the question, what will be the optimal quantity and price that maximizes the firm's profits? (include calculations). How is this case different from the previous situation? (18 points)