A zookeeper recently found out that the lion toby needs surgery on one of his paws. After the surgery, he will need to be isolated from the rest of the lions for a short period of time. The zookeeper decides to build a small cage to house Toby while he recuperates. The zoo has a budget of $30,000 to build a cage with as much volume as possible. The cage will rest on the floor of the lion enclosure, so it does not need a bottom. The material for the ceiling and walls of the cage costs $12 a square foot. Suppose the height of the cage is z feet and the base of the cage is x feet by y feet. In this problem, we want to ___the function___. Our constraint equation is ___.