The Student Internship Director Needs as Much Coverage as Possible

The student internship director needs as much coverage as possible in the office next week. The more hours that can be put in each day, the better. She has asked the students to provide a list of how many hours they are available each day of the week. Each student can be there on only one day and there must be a student in the office each day of the week. Use the table below and the tables provided to determine the schedule that gives the most coverage. Note that the objective of this problem is to maximize the hours worked, not minimize.
$$\begin{array} { | c | c | c | c | c | c | } \hline \text { Student } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thurs } & \text { Fri } \\\hline \text { A } & 2 & 4 & 8 & 4 & 6 \\\hline \text { B } & 3 & 2 & 7 & 3 & 2 \\\hline \text { C } & 6 & 8 & 6 & 5 & 4 \\\hline \text { D } & 7 & 4 & 3 & 6 & 8 \\\hline \text { E } & 4 & 5 & 3 & 1 & 4 \\\hline\end{array}$$