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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 that the alternative allocations for each course would yield the number of grade points shown in the following table: Study Days 1 2 3 4 1 1 3 6 8 Estimated Grade Points 2 5 6 8 8 Course 3 4 6 7 9 4 4 4 5 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 that the alternative allocations for each course would yield the number of grade points shown in the following table: Study Days 1 2 3 4 1 1 3 6 8 Estimated Grade Points 2 5 6 8 8 Course 3 4 6 7 9 4 4 4 5 8

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. 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 that the alternative allocations for each course would yield the number of grade points shown in the following table: Stage 4: n = 4 Stage 3: n = 3 Xn These four courses can be considered as the four stages in a dynamic programming formulation. The decision variables (n = 1, 2, 3,4) are the number of days to allocate to stage (course) n. Let S = number of days still available for allocation to remaining courses (n,...,4). Stage 2: n = 2 Stage 1: n = 1 S4 f4* (S4) 1 2 3 4 X3 S3 x2 S2 S1 7 Study Days Course 1 2 1 5 IMMI 3 6 6 8 8 8 X1 1 2 3 Estimated Grade Points 4 (a) Draw a graphical display of this problem, showing the possible states at each stage, the possible transitions in states, and the corresponding contributions to the measure of performance (grade points). (b) Use dynamic programming to determine how many of days should be assigned to each of the four courses to maximize the total grade points. Please use the tables given below. 3 X4 4 6 7 9 ƒ3(S3, X3) = P3(x3) + ƒ4* (S3 − X3) 4 ƒ₂ ($₂,x₂) = P₂ (x₂) + ƒ3 (S₂ − x₂) f₁($₁, x₁) = P₁(x₁) + f₂ (≤₁ − x₁) 4 4 5 8 f3* (S3) x3 f2* (S₂) x₂ fi (S₁) x₁
Transcribed Image Text:2. 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 that the alternative allocations for each course would yield the number of grade points shown in the following table: Stage 4: n = 4 Stage 3: n = 3 Xn These four courses can be considered as the four stages in a dynamic programming formulation. The decision variables (n = 1, 2, 3,4) are the number of days to allocate to stage (course) n. Let S = number of days still available for allocation to remaining courses (n,...,4). Stage 2: n = 2 Stage 1: n = 1 S4 f4* (S4) 1 2 3 4 X3 S3 x2 S2 S1 7 Study Days Course 1 2 1 5 IMMI 3 6 6 8 8 8 X1 1 2 3 Estimated Grade Points 4 (a) Draw a graphical display of this problem, showing the possible states at each stage, the possible transitions in states, and the corresponding contributions to the measure of performance (grade points). (b) Use dynamic programming to determine how many of days should be assigned to each of the four courses to maximize the total grade points. Please use the tables given below. 3 X4 4 6 7 9 ƒ3(S3, X3) = P3(x3) + ƒ4* (S3 − X3) 4 ƒ₂ ($₂,x₂) = P₂ (x₂) + ƒ3 (S₂ − x₂) f₁($₁, x₁) = P₁(x₁) + f₂ (≤₁ − x₁) 4 4 5 8 f3* (S3) x3 f2* (S₂) x₂ fi (S₁) x₁
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