Linear programming problem

ULIUILIIIJ' Ill IJU ULHUUUUUFU- 1 (5 points). A college student has 7 days remaining before nal 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, 31 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 that the alternative allocations for each course would yield the number of grade points shown in the following table: Estimated Grade Points Course Study Days 1 2 3 4 1 3 5 2 6 2 5 6 5 7 3 6 6 7 9 4 7 8 8 9 Your work must include the following: (a) The adjacency matrices for the multistaged bipartite graph. (b) Every algebraic step for the backward algorithm. (0) If she only wants to spend 1 day on course #1, what is the optimal outcome for this scenario? You must derive the solution from the same work already performed from (b)