Problem $2\mathrm{.}5$ on page $76.$

$2\mathrm{.}5$ The following table, based on data reported in the literature $[$HEAT$84],$ shows the

execution times, in seconds, for five different benchmark programs on three machines.

a$.$ Compute the speed metric for each processor for each benchmark, normalized to

machine R $.$ That is$,$ the ratio values for R are all $1\mathrm{.}0.$ Other ratios are calculated

using Equation $(2\mathrm{.}5)$ with R treated as the reference system. Then compute the

arithmetic mean value for each system using Equation $(2\mathrm{.}3).$ This is the approach

taken in $[$HEAT$84].$

b$.$ Repeat part $($a$)$ using $M$ as the reference machine. This calculation was not tried

in $[$HEAT$84].$

c$.$ Which machine is the slowest based on each of the preceding two calculations?

d$.$ Repeat the calculations of parts $($a$)$ and $($b$)$ using the geometric mean, defined in

Equation $(2\mathrm{.}6).$ Which machine is the slowest based on the two calculations?