In practice, applying an optimization to one part of a codebase can require overheads that did not exist in the original execution or even have negative impacts on logically unrelated portions of the code. Consider an already parallel code whose execution consists of SERIAL (S), PARALLEL-COMPUTE (PC), and PARALLEL-SYNC (PS) regions, where, with 1 thread. S-5% PC 90%, and PS 5% of execution time. Assume that the amount of execution required for PS grows linearly with the number of threads but is itself 80% parallelizable, and that PC receives a 1:1 linear speedup with the number of threads.

Find 1. the number of threads that maximizes the performance of this code, and

2. the speedup of a 100% parallelizable PS over 1) for the same number of threads that maximizes the performance of 1)

(note - no knowledge of parallel threading or synchronization is required to solve this problem -it is a direct application of Amdahl's law)