Jane’s Cakes prepares pound cakes and carrot cakes. In a given week, at most 100 cakes can be prepared, of which 25 pound cakes and 15 carrot cakes are required by regular customers. The profit from each pound cake is $6, and the profit from each carrot cake is $8. How many of each type of cake should be prepared in order to maximize the profit? What is the maximum profit?