Code to resolve a math/logistics problem

I need someone to code (in C#) a solution to fix the following problem: - We have a list of Exhibitions that our people can attend. Each exhibition starts in a date (for example 20th June 2013) and has a specific length in days (for example 6 days). - We have a fixed number of people who can attend the Exhibitions. Many exhibitions are simultaneous. For example: - Exhibition A on the 5th of June lasting 10 days (5th June to 14th June) - Exhibition B on the 7th of June lasting 3 days (7th - 9th June) - Exhibition C on the 10th of June lasting 9 days (10th-18th June) If we only have 1 available person, then we would not be able to attend all of them. Our aim is, given a fixed number of available people (must be dynamic), maximize the number of days attended (not the number of exhibitions, but the total number of days). For example, in this case, if we only have one person available, the best way would be to attend Exhibition B and C which would give us a total of 12 days. If we attend Exhibition A, we would not be able to attend the other two and would only have a total of 10 days. Some conditions: - Each person can work 365 days per year. - Each person is available to start a new exhibition on the first day after his last exhibition finishes - The person who starts one exhibition must be there for it's total duration, he can not attend part of the exhibition, he can either attend it completely or skip it completely. This would be easy if the list of exhibitions was only of 10 elements. However, we have about 70 exhibitions scheduled until the end of 2013. My first approach was: 1 - Generate a list of all the possible combinations 2 - Remove impossible combinations (basically when there are days where there are more simultaneous exhibitions than the number of available people) 3 - Calculate the total number of days in each combination and find the one which gives us more days. However, I got blocked on step 1. The number of combinations is 2^n, so 2^70 is a number extremely large and it was taking hours and hours for the computer to just calculate the combinations, not even considering steps 2 and 3. Then I tried to make an intelligent algorithm that worked like a tree, but it was getting extremely complex and I stopped it. One of the requisites of this code is that it is able to produce an answer (which exhibitions should be attented in order to maximize the total number of exhibitions days given a specific number of available people) in a useful time (some minutes maximum). It should be able to calculate it for a number of exhibitions up to 150 and for a number of available people from 1 to 10. There is no need for graphics or anything. You will just need to create a function where you receive in the input parameters an "Int" with the number of available people and a list of exhibitions. An exhibition is basically a class with a startDate (DateTime), id (String) and length (int), nothing more.