$($i$)$ One person using a hammer will take five days to nail new shingles onto the roof of a $\backslash (300\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ house.

$($ii$)$ Two people using one hammer but working together $($one holds a shingle, the other swings the hammer$)$ will take two days to do the same job.

$($iii$)$ One person using a nail gun will take one day to do the same job.

a$.$ Determine a labour productivity measure and its value for each of the above cases.

$($i$)\backslash (\backslash$quad $60\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ per worker per day

$\backslash$begin$\{$tabular$\}\{$l$|$r$\}$

$($iii$)$ & $75\backslash \backslash$

& $\backslash (\backslash$mathrm$\{$~m$\}^\{2\}\backslash )\backslash \backslash$

$\backslash (\backslash$mathrm$\{$~m$\}^\{2\}\backslash )$ & per worker per day

$\backslash$end$\{$tabular$\}$

$\backslash ($ m$^\{2\}\backslash )$ per worker per day

b$.$ Calculate the percentage increase in productivity due to method improvement from $($i$)$ to $($ii$).$

Productivity $3\backslash \%$

c$.$ Calculate the percentage increase in productivity due to technology from $($i$)$ to $($iii$).$

Productivity $]\backslash \%$