You need to pick between them. Where the first will be the rather obvious "explain and critique" sort of prompt, the second will require you to attempt to apply the theory to a particular scenario and evaluate it in its application--this will also require that you explain and critique, just with a different focus.

You can choose which you prefer or if there is some other topic you are interested in writing on related to what we have been discussing you are free to do so (I only ask you consult me first).

Prompt One:

Explain Mill's utilitarian moral theory and offer an argumentative critique or defense of that position.

Prompt Two:

Read the following story of a unique moral dilemma [from the philosopher Bernard Williams--the essay from which it is taken is also in the book] and then (1) explain, in good detail, what Mill would argue Jim should do, (2) explain why Mill's theory would demand such a response and (3) argue whether or not that account of the situation makes moral sense of that decision [that is, even if you think that utilitarianism tells us to do the right thing, is it right because of utility and the greater good or for some other reason?]. In answering the 1 and 2, I expect a reasonably detailed account of the basic moral theory of Mill/Utilitarianism as an answer to the normative question.

The moral dilemma:

"Jim finds himself in the central square of a small South American town. Tied up against the wall are a row of twenty Indians, most terrified, a few defiant, in front of them several armed men in uniform.

A heavy man in a sweat-stained khaki shirt turns out to be the captain in charge and, after a good deal of questioning of Jim which establishes that he got there by accident while on a botanical expedition, explains that the Indians are a random group of the inhabitants who, after recent acts of protest against the government, are just about to be killed to remind other possible protestors of the advantages of not protesting.

However, since Jim is an honoured visitor from another land, the captain is happy to offer him a guest's privilege of killing one of the Indians himself. If Jim accepts, then as a special mark of the occasion, the other Indians will be let off. Of course, if Jim refuses, then there is no special occasion, and Pedro here will do what he was about to do when Jim arrived, and kill them all.

Jim, with some desperate recollection of schoolboy fiction, wonders whether if he got hold of a gun, he could hold the captain, Pedro and the rest of the soldiers to threat, but it is quite clear from the set-up that nothing of that kind is going to work: any attempt at that sort of thing will mean that all the Indians will be killed, and himself. The men against the wall, and the other villagers, understand the situation, and are obviously begging him to accept. What should he do?"