09-4 A student must select 10 elective courses from four different departments. She must choose at least one course from each department. Her objective is to "allocate" the 10 courses to the four departments so as to maximize her "knowledge" in the four fields. She realizes that if she takes over a certain number of courses in one department, her knowledge about the subject will not increase appreciably either because the material becomes too complicated for her comprehension or because the courses repeat themselves. She thus mea- sures her learning ability as a function of the number of courses she takes in each department on a 100-point scale and produces the following chart. (It is assumed that the course groupings satisfy the prerequisites for each department.) Formulate the problem as a dynamic programming model using both the forward and backward recursive equations. Number of Courses Department 1 2 3 4 5 6 7 8 9 10 H 25 50 60 80 100 100 100 100 100 100 II 20 70 90 100 100 100 100 100 100 100 III 40 60 80 100 100 100 100 100 100 100 IV 10 20 30 40 50 60 70 80 90 100 0 9-5 Solve Problem 9-4 by using the forward and backward recursive equa- tions of DP. Define the states and their feasible range of values for each stage