Question $2(50\%)-$ Consider a program that is used to compute the multiplication of matrices

of large sizes. The program was run on a serial computer, and it took $400$ seconds to execute.

To accelerate the computation process, the program was rewritten to support parallel

computing, and then run on a parallel computer system with $6$ processors. The chart below

shows the utilization $($green color$)$ of the six processors, where the last processor finished

the execution after $80$ seconds from the beginning of the program run.

Determine the speedup achieved by the parallel execution using the six processors

compared to the serial execution. Also, compute the efficiency.

Under ideal conditions, the parallel execution should be $6$ times faster compared to

the serial execution $($ideal speedup $=6)$ and the efficiency should be $1($ideal efficiency

$=1).$ Compare the speedup and efficiency values that you computed in point $1$ with

the ideal speedup and efficiency values. What are the reasons that make the speedup

and efficiency values that you have computed different than the ideal speedup and

efficiency?

Assume that the parallel program is run on $12$ processors to reduce the execution

time, does this lead to changing the speedup and efficiency values that you have

computed in point $1?$ Justify your answer.