5. (Bonus Problem: 8) A college student has 7 days remaining before final examinations begin in her four courses, and she wants to allocate this study time as effectively as possible. She needs at least 1 day on each course, and she likes to concentrate on just one course each day. So, she wants to allocate 1,2,3, or 4 days to each course. Having recently taken an OR course, she decides to use dynamic programming to make these allocations to maximize the total grade points to be obtained from the four courses. She estimates the number of grade points that each alternative allocation would yield as shown in the following table: Solve this problem by dynamic programming. Specify stages, states, decision variables, the interpretation of the value function, its recursive relationship, the optimal value function, and solve the dynamic program via backward induction (show the intermediate steps of the solution procedure). Identify the optimal allocation and the optimal grade points to expect