According to John Stuart Mill philosophy of Utilitarianism, "one should always do something that makes many people have the greatest happiness with a reason" (Mill 33). Mill believe that the most ethical thing to do in any situation is the one which brings most happiness to a greater number of people. This means the less people who might be hurt in the process of utilitarianism is not as important. Therefore in this situation of a madman threatening to explode several bombs, Mill would advice to do anything possible to prevent the bombs from exploding. It is most ethical to save a greater number of people who could otherwise be killed by the explosion of the bombs than to save the madman from torture (Mill 37-40).
Mill would advice, according to his "greatest-happiness principle" (Mill 33), that is the best action to perform if to use torture and authority to make the madman divulge the location of the bombs so as to stop explosion (Mill 34). Since the conventional methods cannot work in this situation of making him reveal the location of the bombs. This may not be allowed by law, however this is a desperate situation which will lead to a great harm if not prevented. Mill argues that happiness has a greater value than contentment. Therefore the people who will be killed by the bomb explosion have more value than the madman. In this case any form of torture can be subjected to the madman as long as he reveals the location of the set bombs. This is called quantitative approach to ethics (Mill 42).
In conclusion the best thing to do is to ensure that the madman divulges the location of the bombs in the shortest time possible. It is morally ethical to subject him to torture for the benefit of a higher number of people and property that have more value than him (Mill 34). The authority should therefore torture him despite the limitations of law for the reason of the greatest-happiness principle.