Suppose a program is divided into $7$ tasks. One task at the beginning must be executed by itself

$($i$.$e$.$ with no other tasks in parallel with it$)$ and takes $3$ms$.$ Also, there is a task at the end of the

program that must be executed by itself and takes $4$ms$.$ Between these two tasks, there are $5$ tasks

that can be executed simultaneously and each of these tasks takes $16$ms$.$

a$.[2]$ What is maximum speed$-$up according to Amdahl$$s law? $[$Hint: Calculate F$,$ which

is the fraction of sequential part, as a fraction of time of the span to the total execution

time$]$

b$.[2]$ What is the largest number of cores we can use after which no speedup will be seen?

Justify.

c$.[2]$ If we use the largest number of cores you calculated in the above question, what is

the speedup we get? Do not use Amdahl's law in your calculations in this question.

d$.[2]$ Is there a difference between the speedup you calculated in $$c$$ and $$a$$ above?

Justify