$5-$ A crawler bulldozer weight $20$ tons is used to push a soil $($swell $25\backslash \%)$ for a distance $100$ m with a grade $\backslash (4\backslash \%\backslash )$ and Rolling R$.\backslash (80\backslash$mathrm$\{$~kg$\}/\backslash )$ ton, has the following specifications:

$-$ Blade length $2\mathrm{.}5$ m and height $0\mathrm{.}8$ m with a soil grade in front of the blade $1$:$2$

$-$ Speed in pushing $\backslash (2\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$hr$\}\backslash )$ and $\backslash (4\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$hr$\}\backslash )$ in return with a fixed time $1\mathrm{.}5$ minutes

$-$ The equipment stops $12$ minutes$/$hour$,$ and works $6$ hours$/$day$.$ Determine:

A$-$ The productivity for $4$ days

B$-$ The number of bulldozers needed to push $\backslash (768\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ within $5$ days