Gracilyn's Gourmet Sweets prepares coffeecakes and cheesecakes for restaurants. In a given week, at most 100 cakes can be prepared, of which 25 coffeecakes and 15 cheesecakes are required by regular customers. The profit from each coffeecake is $8, and the profit from each cheesecake is $17. How many of each type of cake should be prepared in order to maximize the profit? What is the maximum profit?