(a) (8 points) Class Scheduling: Let S denote the set of students at UTD, and let C denote the set of classes. For a student x E S, let C(x) denote the set of classes that student r is interested in taking. The school policy is that each student can take at most 5 classes per semester. Additionally, each class can have at most 20 enrolled students. Naturally, a student can register for specific class at most once. The University's goal is to maximize class enrollment, i.e. the sum over all classes of the enrolled total in each class. (Note this may mean some students won't be able to register for any courses, and some courses may be empty.) Describe how to use maximum flow to meet this goal, that is you need to specify the vertices, edges, and capacities in a flow network. (a) (8 points) Class Scheduling: Let S denote the set of students at UTD, and let C denote the set of classes. For a student x E S, let C(x) denote the set of classes that student r is interested in taking. The school policy is that each student can take at most 5 classes per semester. Additionally, each class can have at most 20 enrolled students. Naturally, a student can register for specific class at most once. The University's goal is to maximize class enrollment, i.e. the sum over all classes of the enrolled total in each class. (Note this may mean some students won't be able to register for any courses, and some courses may be empty.) Describe how to use maximum flow to meet this goal, that is you need to specify the vertices, edges, and capacities in a flow network