Reasons for thinking that morality must have a first principle

Write a coherent, well-crafted essay that does the following things:

(a) Describe J. S. Mill’s principle of utility.  (b) Explain what Mill means when he says that the principle of utility is the “First Principle” of morality and explain Mill’s reasons for thinking that morality must have a first principle.  (c) Distinguish direct utilitarianism from indirect utilitarianism.  (d) Describe Bernard Williams’ hypothetical case in which “George the chemist” faces a moral dilemma.  (e) Does the case of George the chemist show that some forms of utilitarianism are false, mistaken, or that they provide us with a poor guide to action?  (fi) If you think the example undermines some forms of utilitarianism, describe which and explain why you think the example undermines these forms of utilitarianism. (fii) On the other hand, if you think the example fails to undermine any form of utilitarianism explain why you think this is so. (g) How might an indirect utilitarian who still thinks that promoting happiness is the point of morality justify acting in accordance with a rule (on a particular occasion) when he knows that if he made an exception to that rule on that particular occasion alone this would lead to more happiness than would result if he did not make an exception on that occasion?

The paper must be 5 pages long, double-spaced text in normal font (e.g. Times New Roman 12 pt.), with normal tabs and margins (e.g. Microsoft Word’s default settings).