Profit maximizing price and output for monopoly

A monopolist has the total cost function C=3Q2 (thus marginal cost is MC=6Q) and faces a demand curve P=1,200-Q (thus marginal revenue is MR=1,200-2Q).

a) Illustrate what is the profit-maximizing price and output? What is the total profit? What is the price elasticity of demand at the profit maximizing output?

b) On a graph, represent the demand curve faced by the monopolist, as well as the MR, MC and AC curves. Clearly show in the graph the price, output and profits from part a).

c) There is a change in tastes by which the demand for the good that the monopolist sells becomes more elastic. The monopolist realizes than even with this new demand function, it will maximize its profits by producing exactly the same output as in part a). However, its market research shows that the price elasticity of demand at that output is -8. Which will be the new price and profits for the monopolist?

d) Why can't the monopolist charge the same price in part c) as in part a)? describe clearly the economic intuition behind your answer.