According to act utilitarianism, if it produces more net utility (or "happiness") to give money to famine relief, even though I had promised to pay back a friend with that money, then I ought to give the money to the relief fund.

a. true
b. false

This is TRUE.

Explanation: According to Utilitarianism principle of utility, it states that any decisions, actions, or behavior been choosed by anyone is right, if it satisfy such persons happiness or pleasure, and wrong if it doesn't satisfy the person's happiness nor pleasure. Many utilitarians believe that pain and pleasure are what we decide by our actions.

From the question, even though a promise has been made to pay back a money borrowed, but because more happiness will be found by giving it to the relief found, it is therefore right to give it to the relief found. It doesn't matter if promises are broken. Any thing that makes one happy is right. This is true about Utilitarianism.