Lucy has a dog and she wants his food to be mixed.  In order to keep the dog healthy but also keep the food tasty, the mix needs to have a minimum of 15 units of calcium, 20 units of vitamin mix, and 20 units of protein. A regular brand costs $20 per bag and contains 4 units of calcium, 7 units of vitamin mix, and 10 units of protein. A premium brand costs $35 per bag and contains 12 units of calcium, 10 units of vitamin mix, and 16 units of protein. How many bags of each brand should Lucy mix in order to minimize cost while also meeting the taste and health requirements.