Lisa is making cookies to sell at the annual Dirt Bike Competition. A dozen oatmeal cookies require 3 cups of flour and 2 eggs. A dozen sugar cookies require 4 cups of flour and 1 egg. She has 40 cups of flour and 20 eggs. She can make no more than 9 dozen oatmeal cookies and no more than 7 dozen sugar cookies. She earns $5 for each dozen of oatmeal cookies and $4 for each dozen of sugar cookies. How many dozens of each type of cookie should she make to maximize her profit? What will her maximum profit be?