Help me solve this real problem from my workplace.

We want to kill the oldest subset of these N people in a way that....

The above is a problem I came to when designing time series in a charting library...

What a rollercoaster ride!

a0,a1,.....aN means there are N+1 people not N people.

• Can the "age" of any "people" be negative (or zero)?
• Are you sure that you want to get the subset of maximum sum instead of maximum count? I just looked up "time series", and think that it makes sense to ask for maximum count, but not sure what maximum sum is for.
• I suppose approximate solution is allowed? This is a "real-life" problem, after all.
• Actually, mathematical description is usually preferred. (Given a sequence of numbers,...) Background can be interesting to read sometimes, but it's usually more annoying.
• There's an obvious O(n^3) dynamic programming solution, and it can be optimized to O(n^2) with some effort. However in case there's some special condition on p or q (such as p<=10 or q<=10 or n/p<=10 or q/p<=10 ...) the algorithm can be more efficient. What's the real use case?

Is this money heist?