$.($i$)$ One person using a hammer will take $5$ days to nail new shingles on the roof of a $300$ m$2$ house. $($ii$)$ Two persons using a hammer but working together $($one holds a shingle, the other swings the hammer$)$ will take $2$ days to do the same job. $($iii$)$ One person using a nail gun will take $1$ day to do the same job. a$.$ Calculate the labour productivity $($in m$2$ per worker per day$)$ for each of the above cases. b$.$ Calculate the $\%$ change in productivity due to method change, i$.$e$.,$ from $($i$)$ to $($ii$).$ c$.$ Calculate the $\%$ change in productivity due to using technology, i$.$e$.,$ from $($i$)$ to $($iii$).$