Given a list of jobs with length lets say varying from 5 to 200 minutes with different profit rates per job. How would one calculate maximum profit from the original set of jobs while the duration of the jobs combined equals to a given value (for example 500).
There can be many jobs of same length but different profit rates.
Let $\pi_i$ be the profit per minute for job $i$ and $T_i$ be the minutes spent on job $i$. There are $n$ jobs. If I understood your question correctly, your aim is to solve
$$\max _{T_i\in [5,200]}\pi_1T_1+...+\pi_nT_n\\ \text{s.t. } T_1+...T_n=500.$$
Assume without loss $\pi_1\geq \pi_2...\geq \pi_n.$ Then the optimal solution is to dedicate as many minutes to the highest profit-per-minute job as possible, then dedicate as many minutes to the next highest profit-per-minute job as possible, etc. until you exhaust your budget.
In your case, assuming $n\geq 3$, this means the optimal solution is $$T_1^*=200,T_2^*=200,T_3^*=100,T_k^*=0,k\geq 4.$$