This paper extends the classic Lanchester representation of a battle between an Attacker and a Defender to the case where the former possesses two weapon types, and the latter one. The Defender's force levels can be reduced by both types of Attacker weapons but at different attrition rates. The converse also applies. Victory is assumed to be by total annihilation of the Defender, towards which the battle progresses in one of two ways: where the Attacker is left with some of both weapon types, or where he retains some of one type only. The analysis is then extended to cover the optimization problem of minimizing the Attacker's initial resources. The implications for casualties are also discussed.