Let 'x' and 'y' be integers, with x + y = 100. When run on a serial computer,

portion A of program PROG consumes x% of the time, while portion B consumes

the remaining y%. When run on a parallel computer, portion A speeds up

by a factor of 4, while portion B speeds up by the number of processors P.

P = 906 is the smallest number of (integer) processors required to achieve

at least 7/8 of the theoretical maximum speedup.

a) What are the values of 'x' and 'y'? If you knew the values of 'x' and 'y',

you could compute the (real) number of fractional processors P_frac required

to achieve exactly 7/8 of the theoretical maximum speedup, and then compute P

as the ceiling of P_frac. Since P = 906, 905 < P_frac <= 906. Simple algebra

allows you to express P_frac as a function of 'x'. It is then easy to guess

the value of 'x', and verify that P_frac lies in the specified interval.