A sleeve coupling connects two solid shafts in a motor and pump assembly. The following information is provided:

Power transmitted by the motor:

P $=50$kW

RPM $($N$)=1440$ RPM

Permissible shear stress for the shaft material: Tshaft $=45$ MPa

Permissible shear stress for the sleeve material: Tsleeve $=30$ MPa

Find the diameter of the solid shaft $($d$),$ the outer diameter $($D$),$ the length of the sleeve $($L$),$ and the dimensions of the key $($width w and height h$).$