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When it is not economical to carry out maintenance in-house, out-sourcing to an external agent is an alternate viable option. In this paper, we study a simple maintenance service contract involving a single agent (providing the maintenance service) and a single customer (owner of the equipment and recipient of the maintenance service). We develop a simple model to obtain the optimal strategies for both the customer and the agent. We give a complete characterization of the strategies along with some sensitivity analysis and discuss some extensions.