Question

Run serially, portion A of program P consumes 33 s, while portion B
consumes 925 s. On a parallel computer, moderately serial portion A speeds up four times, while perfectly parallel portion B speeds up by the number of processors. i) What is the speedup of program P on 1,024 processors? ii) How many processors are required to achieve at least half the theoretical maximum possible speedup on P?

For i), I did:

Serial run-time of A: A_serial = 33s
Serial run-time of B: B_serial = 925s
Parallel run-time of A = A_parallel = A_serial/A_speedup = 33s/4 = 8.25s
Parallel run-time of B = B_parallel = B_serial/# processors = 925s/1024 = 0.90s

Serial run-time = T_serial = A_serial + B_serial = 33s + 925s = 958s
Parallel run-time = T_parallel = A_parallel + B_parallel = 8.25s + 0.90s = 9.15s
Total speedup = T_old/T_new = T_serial/T_parallel = 958s/0.90s = 104.66

Therefore, program P speeds up 104.66 times? Is this correct? Also, I wanted to know, since it seems from many sources that the theoretical maximum speedup is 20, can the calculated speedup ever be greater than 20? Because that is the result I got for this problem (104.66, which is >20). And what exactly does "moderately serial" mean?

For ii):

max speedup = 20 -> half max speedup = (50%)(20) = 10
10 = T_serial/T_parallel = 958s/T_parallel -> T_parallel = 958s/10 = 95.8s
95.8s = A_parallel + B_parallel = 8.25s + 925s/# processors -> # processors = 925s/(95.8s - 8.25s) = 10.57 processors