Why did Prospeo and Miranda not abandon Caliban instead of keeping him as a slave?

Prospero would love nothing more than to keep Caliban as slave. Miranda, however, wishes to educate him. Caliban is misunderstood and treated poorly, but he has also made some pretty hefty mistakes (attempting to rape Miranda). None-the-less, we see that Miranda is willing to look at the circumstances that create the man, and her hopes that he can be something more.