$10.$ A program executes on a multiprocessor system and computes a vector product

containing one hundred $32-$bit integer elements P$[$i$].$ Each element in the vector

product is computed as P$[$i$]=$A$[$i$]*$B$[$i$]$ where A and B are both vectors that contain

one hundred $32-$bit integer elements. It takes $1$ clock cycle to compute each element

in the array P$.$ After the vector product is computed, the program computes a matrix

product by multiplying every $32-$bit integer element in a matrix by a $32-$bit integer

constant. The matrix contains $1000$ rows and $1000$ columns. Multiplying a single

matrix element by the constant takes one clock cycle.

a$)(5)$ Ignoring the time required to manage any loops, what is the total number of

clock cycles required by the single processor to compute both products: the vector

product followed by the matrix product?

b$)(5)$ The same program is executed again, this time with a total of $200$ identical

processors. There are no memory conflicts caused by the processors sharing memory

and there are no other dependencies, so no stalls are necessary. If the workload is

divided as evenly as possible among the $200$ processors, what is the total number of

clock cycles required to compute both the vector product followed by the matrix

product on the $200-$processor system? Ignore the time required to manage any loops