Solution

Gustafson's law:

S_{p} = \frac{W_{s} + p \cdot W_{p}}{W_{s} + W_{p}} = p - λ (p - 1)

where the speedup $S_{p}$ depends on

The whole work $T = W_{s} + W_{p}$ is the the work that can be executed by one processor in $T$ time.

Amdahl's law (with $λ = 0.2, p \to \infty$ ):

S_{\infty} = \frac{1}{λ} = \frac{1}{\frac{1}{5}} = 5

The maximal achievable speedup is $5 \times$ .

with $λ = 0.06, p = 47$ :

S_{p} \leq \frac{1}{λ + \frac{1 - λ}{p}} = \frac{1}{\frac{3}{50} + \frac{1 - \frac{3}{50}}{47}} = \frac{1}{\frac{3}{50} + \frac{1}{50}} = \frac{50}{4} = 12.5

The maximal achievable speedup is $12.5 \times$ .