The use of a heat pump to utilise the waste heat from a heat engine has been studied. The optimal heat delivered and the optimal heat pump to heat engine work ratio has been determined for externally and totally irreversible heat engines and heat pumps. The results show that the highest temperature at which the heat is delivered from the heat pump must be less than 1.125 T-12 The power used in driving the heat pump consumes more than 60% of the output power from the heat engine (the upper limit is 100%).