Hog's Head ownership is deciding what price to charge for pumpkin juice and butterbeer to maximize its profits. Let a be the price of pumpkin juice and b be the price of butterbeer, both in sickles (currency from the magical world). The demand equations are

x = 97 30a + 5b

y = 106 + 3a 20b

where x is the number of pumpkin juices sold in a day and y is the number of butterbeers sold in a day. Their daily costs are C = a + 2b + 50 sickles. How much should Hog's Head charge for each item to maximize their daily profits? Include units. Be sure to test that these give you a maximum.