$3.(25$ points$)$ A HKUST 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 $\backslash (1,2,3\backslash ),$ or $4$ days to each course. Having recently taken prescriptive analytics 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 that the alternative allocations for each course would yield the num ber of grade points shown in the following table:

Solve this problem by dynamic programming.