This is an optimization algorithm that selects the best projects based on a given profit and cost for each

As the chief project manager of the team, one task of yours is to select a set of projects for the team. Suppose each project i is associated to a pair of values ci and ri, where ci is the cost to work on project i and ri is the revenue of project i after completion. Assume your team start with a capital value c, and you can only select one project with its cost not exceeding your team’s capital. Upon completion of the project i, your team’s capital will increase by the profit of that project, which is ri-ci . You may also assume your team only work on one project at a time, and projects are all valid with ri ≥ ci ≥ 1 . Given the set of projects, an initial capital value c, and k the number of projects to be selected. You are to work out a selection plan such that the final capital is maximized.

Why this exercise?

1. To learn more about Dynamic Programming algorithms
2. To be able to use and optimize the solution of a problem
3. DP is used in many optimization problems in the real world. This case help in cost minimization and improve results for projects involving selection.