Charlie Dolittle has 5 days to prepare for final exams in three courses. His met
ID: 454992 • Letter: C
Question
Charlie Dolittle has 5 days to prepare for final exams in three courses. His method of studying requires that he study one and only one course each day. The entries in the following table give his estimate of the final exam score for each of the courses if he studies that course for the number of days in the left-hand column .see the tabel
charlie want to allocate his five study days to the three courses so to maximize the sum of his estimated final exam scores.
(a) Formulate this problem as a dynamic programming problem. Use the notation developed in the chapter and be sure to indicate what the stages and states are as well as carefully define fn(s, xn) in words.
(b) Solve this problem using your formulation in part (a)
Final exam score in
Days of study
Course 1
Course 2
Course 3
0
60
70
40
1
65
75
45
2
70
75
45
3
80
80
60
4
85
90
80
5
85
95
90
Final exam score in
Days of study
Course 1
Course 2
Course 3
0
60
70
40
1
65
75
45
2
70
75
45
3
80
80
60
4
85
90
80
5
85
95
90
Explanation / Answer
Name of the book is not mentioned, therefore notations may be different.
charlie want to allocate his five study days to the three courses so to maximize the sum of his estimated final exam scores.
Therefore decision variables are number of days allocated to the courses and objective is to maximize the total exam scores. Let Xij represents the allocation of 'i' number of days allocated to jth course and Sij is the corresponding exam scores. Xij is binery taking the value 1 if selected otherwise 0.
From above the maximum score (220) is for spending 5 days on course 3.
Alternatives/options Obj.Coef. 60 70 40 65 75 45 70 75 45 80 80 60 85 90 80 85 95 90 SumProd. Course1 Course2 Course3 Total days X01 X02 X03 X11 X12 X13 X21 X22 X23 X31 X32 X33 X41 X42 X43 X51 X52 X53 Total Scores 0 5 0 5 1 1 1 195 0 4 1 5 1 1 1 195 0 3 2 5 1 1 1 185 0 2 3 5 1 1 1 195 0 1 4 5 1 1 1 215 0 0 5 5 1 1 1 220 1 4 0 5 1 1 1 195 1 3 1 5 1 1 1 190 1 2 2 5 1 1 1 185 1 1 3 5 1 1 1 200 1 0 4 5 1 1 1 215 2 3 0 5 1 1 1 190 2 2 1 5 1 1 1 190 2 1 2 5 1 1 1 190 2 0 3 5 1 1 1 200 3 2 0 5 1 1 0 1 195 3 1 1 5 1 1 1 200 3 0 2 5 1 1 1 195 4 1 0 5 1 1 1 200 4 0 1 5 1 1 1 200 5 0 0 5 1 1 0 1 195