MATH**02/72** Operations Research & Mathematical Planning 2024
Tutorial 8 – Dynamic Programming
Python Functions 
Define functions in Python to
• Calculate the factorial of a number n
• Calculate the value function for the ‘Minimal Studying’ problem
• Determine the optimal solution for the ‘Minimal Studying’ problem

Knapsack Problem 
We have a container of size 20 units, and want to pack it with the following 
valuable items:
Item j  Size vj  Value tj
How many of each item should we pack in order to maximize the total value?
Fibonacci Sequence 
Define a function in Python to calculate the number in the Fibonacci
sequence.
 
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