At a university, a student is organizing a study group and is inviting his classmates Adrian and Broghan to help him solve problems. Adrian solves 2 problems per hour and requires 1 cup of coffee per hour and 2 cookies an hour. Broghan solves 3 problems per hour and requires 2 cups of coffee an hour and 1 cookie an hour. A cup of coffee costs $3 and a cookie costs $6. Each of the students is not able to work for more that 7 hours due to course work and other commitments, and each of them requires to be involved for at least one hour. If this student estimates that he will need help with at least 11 problems, for how many hours should he invite Adrian and Broghan to minimize the cost of purchasing snacks