A mine desires to select a front$-$end loader to re$-$handle a stockpile at

a rate of $450\frac{t}{h}r.$ The anticipated loading, manoeuvring and dumping

time is $45$ seconds and the F$.$E$.$L$.$ will travel at an average speed of $3\mathrm{.}9$

$k\frac{m}{h}r$ to dump its load and return for another load over a distance of

$15$ m $.$ Bucket fill factor is estimated as $0\mathrm{.}9$ and material loose density

is $2\mathrm{.}2\frac{t}{m}3.$ If machine availability and utilization are expected to be

$0\mathrm{.}75$ and $0\mathrm{.}8$ respectively, determine a suitable bucket size.