Dynamic Programming About Uses in DP Examples of DP See Also References
Besides computer programming this technique can be used in: A common usecase in math are the Bellman equations which use a recursive relationship between value functions to calcutate the value of y from the value functions at i-1. The optimal values for all the decision variables can be found by tracking the calculations at each state.

Backpack Problem: Given a set of treasures with known values and weights, which of them should you pick to maximize your profit whilst not damaging your backpack which has a fixed capacity?

Egg Dropping: What is the best way to drop nn eggs from an mm-floored building to figure out the lowest height from which the eggs when dropped crack?

Longest Common Subsequence: Given two sequences, which is the longest subsequence common to both of them?

Subset Sum Problem: Given a set and a value n,n, is there a subset the sum of whose elements is n?n?

Fibonacci Numbers: Is there a better way to compute Fibonacci numbers than plain recursion?

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Refer to these links for in-depth examples:

Dynamic Economics in Practice

Dynamic Programming in Economics

Refer to these links for in-depth examples and explanations:

Systematic Dynamic Programming

UCSD Bioinformatics Dynamic Programming
Economics

In economics we can also use value functions to maximize/minimize dynamic social welfare problems. Similarly to mathematics we use value functions from previous states in order to find the most optimal solution for solving social economic problems. A good example of this is Ramsey's problem , which in simple terms relates the different levels of utility of a product to the amount of consumption that product takes. An example of this would be for a manufacturer deciding how much to raise the products price so that the revenue equals the total cost of producing the good.

Bioinformatics

In bioinformatics algorithms have been used in the case of RNA structure predicting, protein DNA binding, and sequence alignment. The first algorithm of this kind used in bioinformatics was for protein DNA binding developed by Charles DeLisi in the 1970s. As of lately common areas where dynamic programming is used is in transcription factor binding and nucleosome positioning. Here's an example of how dynamic programming is used in bioinformatics: