Sounds like an optimization problem. I know my calculus book is around here somewhere...

I think you will need to refine your model. At the least, you will have to have some way to limit resting heart rate to be > 0. Alternatively, your model suggests that person will die from 6000 hours of practice, as it would bring his resting heart rate down to zero. If you don't, your optimization run would say something like "work out for 1,000,000 hours at a cost of 100,000,000 heart beats or so. Then, enjoy an infinite life with negative resting heart rate and even lower heart rate during exercise."

You also will want to model the fact that your resting heart rate does not stay at a lower level forever after exercise.

Finally, but that's peanuts compared to the other problems: let's start with a starting rest rate of 60 BPM. Exercise for 1000 hours to bring it back to 50 BPM, and your heart rate during workouts becomes 1.2 x 50 BPM = 60 BPM? Unlikely.

While resting heart rate is determined mostly by how fit you are, and is usually in the 50-80 range, maximal heart rate is generally a factor of your age. The accepted formula for maximal heart rate is (210 - age). Most workouts are at 60-75% of maximal heart rate (depending on workout intensity), so a 20% increase during workout is not likely (or at least, you wouldn't call it a workout).