Coordinates of the five machines A$,$ B$,$ C$,$ D$,$ and E are $(10,7\mathrm{.}5),(20,20),(60,12\mathrm{.}5),(35,7\mathrm{.}5),$ and $(5,20),$ respectively.

$($a$)$ Determine the dimensions of each equipment type.

$($b$)($b$)$ Determine the following distance measures for each equipment

pair:

$($i$)$ Euclidean

$($ii$)$ Squared Euclidean

$($iii$)$ Rectilinear

$($iv$)$ Tchebychev

$($c$)$ Using the distances calculated in part $($b$)$ and frequency of trips between matrix calculated in Exercise $3,$ part $($e$),$ determine the sum of flow times distance for the equipment pairs for each distance metric.