$1.$ A drilling and blasting operation being conducted within a mine, utilizes the following parameters: the blast hole pattern is $12*100$; the holes in the first four $(4)$ rows are drilled to a depth of $8\mathrm{.}5$ m$,$ the next four rows are drilled to a depth of $9\mathrm{.}5$ m and the final four rows to a depth of $10\mathrm{.}5$m with the sub$-$drilling in all of the blastholes being $0\mathrm{.}5$m ; the burden and spacing are $4$ m and $6$ m respectively; the density of the mineral is $2\mathrm{.}3$ t$/$m$3$; the uppermost $1\mathrm{.}25$m in each blast hole consist of stemming material whilst the remaining section of the blast hole is filled with explosives with the charge weight being $6$ kg$/$m; $25$ ms delay detonators are used between holes within the rows and $15$ ms delays are used between rows $($at the two extreme ends$).$ Determine the following:

$($a$)$ the quantity of explosives required for the given blast pattern;

$($b the approximate area of the blast site;

$$the tonnage of broken mineral obtained;

$($d$)$the quantities of $25$ ms and $15$ ms delays required for the given blast pattern.

$($e$)$The minimum duration for all the explosives to detonate following the initiation of the blast. Initiation takes place from the fifth hole in the first row.

$($f$)$ Make a sketch showing the configuration of one of the blast hole from each of the three depths specified.