We describe a mathematical model, developed using the Mathematica programming system of the disposable soma theory of ageing. The model makes explicit predictions about the optimal strategies for investment in somatic maintenance versus investments in growth and reproduction and confirms the central prediction of the disposable soma theory that the optimum investment in somatic maintenance is less than what would be required for indefinite longevity. We also describe how the optimal investment in maintenance is affected by varying the parameters that specify the schedules of reproduction and mortality.