The $440$ V$.3-$ph $60$ Hz a$.$c$.$ shaft generator of a ship supplies the following four loads:

$$ Incandescent lighting and heating$-70$ kW

$$ Fluorescent lighting$-50$ kW at $0\mathrm{.}9$ lagging

$$ Navigation aids and miscellaneous$-35$ A at $0\mathrm{.}85$ lagging

$$ Induction motors$-200$ kW at $0\mathrm{.}75$ lagging

$($a$)$ Determine the total kW$,$ kVAr, kVA and overall power factor of the ship$$s load.

$($b$)$ A $3-$ph synchronous motor which takes $50$ kW is now connected to the power system.

Determine:

$($i$)$ the required power factor of this motor to cause the shaft generator to operate at unity power factor.