A college student has 5 days remaining before final examinations begin in her four modules, and she wants to allocate this study time as effectively as possible. She likes to concentrate on just one module each day, so she wants to allocate 0, 1, 2, 3 or 4 days to each module. She estimates that alternative allocations for each module would yield the number of score points shown in the table below. Number of days Module 1 0 0 1 3 2 5 3 7 4 8 Module 2 0 5 5 7 8 Module 3 0 2 6 7 8 Module 4 0 1 2 3 5 (a) Use dynamic programming to find an allocation of study days to modules to obtain the maximal total score. Explain your calculations.
A college student has 5 days remaining before final examinations begin in her four modules, and she wants to allocate this study time as effectively as possible. She likes to concentrate on just one module each day, so she wants to allocate 0, 1, 2, 3 or 4 days to each module. She estimates that alternative allocations for each module would yield the number of score points shown in the table below. Number of days Module 1 0 0 1 3 2 5 3 7 4 8 Module 2 0 5 5 7 8 Module 3 0 2 6 7 8 Module 4 0 1 2 3 5 (a) Use dynamic programming to find an allocation of study days to modules to obtain the maximal total score. Explain your calculations.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A college student has 5 days remaining before final examinations begin in her four modules, and she
wants to allocate this study time as effectively as possible. She likes to concentrate on just one
module each day, so she wants to allocate 0, 1, 2, 3 or 4 days to each module. She estimates that
alternative allocations for each module would yield the number of score points shown in the table
below.
Number of days Module 1
Module 2
Module 3
Module 4
1
3
2
1
2
5
2
3
7
7
7
3
4
8
8
8
5
(a) Use dynamic programming to find an allocation of study days to modules to obtain the
maximal total score. Explain your calculations.
Having recently taken an optimisation models module, the student decided to use linear
programming to find the allocation. She amended the score table in a way that for each module i the
score column can be represented as a linear function a+b;d, where d is the non-zero number of days
allocated, and a; and b; are some constants. She decided that the score is still zero if no study days
are allocated to the module.
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