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This paper proposes a Stackelberg Game Approach to trade-off between maximising the profit of the retailer and minimising the payment bills of the customers. The electricity retailer determines the retail price and sends the price information to customers through an advanced metering infrastructure. According to the announced price, the customers obtain the optimal scheduling details of the appliances in each household through an optimal residential electricity consumption scheduling framework. Once the scheduling details of appliances in each household are obtained, the retailer can maximise its profit by solving the profit maximisation problem. We model the interactions between the retailer and electricity customers as a 1-leader, N-follower Stackelberg Game. At the leader's side, i.e., for the retailer, we use genetic algorithms to maximise the profit while at the followers side, i.e., for customers, we use linear programming techniques (Simplex Method) to optimise the payment bills. Simulation results show the feasibility of the proposed approach.