Explain how a utilitarian might approach the issue of eating animals.

A utilitarian would approach the ethics of eating animals by determining what the effects of eating animals would be. The best conclusion would be the one that maximises utility; the best effects for every subject involved. Depending on what kind of utilitarianism, we can decide whether eating animals is good. Whether we should eat animals depends on which model of utilitarianism is used.
We can argue for, against, or represent multiple views for eating animals. The key is to show sensitivity to differences in different forms of utilitarianism and why that is the case. One argument for eating animals is that it is a beneficial and pleasurable experience for human beings (using Bentham's pleasure principle) that we would not have if eating animals was banned. In this case, they would have to acknowledge that animals are not included in the matrix. Another argument could be made against eating animals on the basis of Moore's idealist utilitarianism, on the basis that we hold ideals against suffering and eating animals would bring suffering to animals that would be detrimental to this ideal. In this argument, it would be important to acknowledge the difference in the definition of utility and who is included in the ethical calculation. The importance is to assert the utility of one argument over the disutility of the other option.