$4.(20$ points$)$ A wheel$-$type dozer $(500$ fwhp$)$ is going up the hill $($uniform slope $\backslash (11\backslash \%\backslash ))$ by steady speed $6$ mph $.$ It is used to pull a truck $($engine shut down$)$ to move soil. This dozer has total weight $95,000$ lbs $($transferred to drive axle $60\backslash \%).$ The truck has empty weight $\backslash (25,000\backslash$mathrm$\{$lbs$\}\backslash ).$ It is loaded $\backslash (25,000\backslash$mathrm$\{$lbs$\}\backslash )$ of soil. The rolling resistance is $\backslash (120\backslash$mathrm$\{$lb$\}/\backslash )$ ton for dozer and $\backslash (100\backslash$mathrm$\{$lb$\}/\backslash )$ ton for truck. These machines are operating at mean sea level. If $20$ lbs of rimpull required a ton of weight per $\backslash (1\backslash \%\backslash )$ of slope $(\backslash (1\backslash$mathrm$\{$ton$\}=2,000\backslash$mathrm$\{$lbs$\}\backslash ))$

$4\mathrm{.}1)$ What is the minimum efficiency of this dozer should develop?

$4\mathrm{.}2)$ What is a minimum coefficient of traction required for working without slipping?

$4\mathrm{.}3)$ If this dozer has gear condition following the given performance chart, what is the maximum rolling resistance of dozer $(\backslash (\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ton$\}\backslash ))$ for steady speed $3$ mph $?$ if rolling resistance of truck is not changed. Give me the step by step explanation of calculation and answers