The load on a vessel$$s distribution system comprises:

$($i$)$ motors totalling $1200$ kW at a p$.$f$.$ of $0\mathrm{.}7$ lag; $($ii$)$ lighting totalling $500$ kW at unity p$.$f$.$: $($iii$)$ an over excited synchronous motor taking $200$ kW at p$.$f$.0\mathrm{.}5$ lead. This total load is shared by two identical alternators, one of which provides $1000$ kVA at a p$.$f$.$ of $0\mathrm{.}85$ lag. Calculate EACH of the following: $($a$)$ the kW supplied by the second alternator; $($b$)$ the kVA supplied by the second alternator; $($c$)$ the power factor of the second alternator;