At Taste of Thyme coffee shop a dirty chai latte creates a profit point of $2.77 for a small and $3.34 for a large. In a month, 245 small lattes were sold and 285 large lattes. As a fast growing demand item with fall approaching, the demand is estimated at 450 and 420 per month. The amount of machine time needed to produce the lattes is 5 minutes and 7 minutes each or for a month, 16.47 hours a month for a small and 33.25 hours a month for a large. What is the maximization function for profit?