The road towards the decarbonization of electricity leads to high deployment of low-carbon power sources including intermittent energy sources. In this context, flexible nuclear power plants could play a significant role because they do not produce CO2 emissions and under certain conditions flexible operation is necessary to ensure the stability of the electricity grid. Flexible nuclear reactors have the ability to load-follow the predicted fluctuations in demand. However, high fixed costs of nuclear production, tighter regulations since the Fukushima accident and the extensive participation of renewable sources in the energy mix challenge the economic profitability of nuclear production. Consequently, a question that arises is how nuclear power producers can manage flexible nuclear production in order to maximize their profits. We proved that optimal production behaviour is not characterized by constant nuclear production unless further investments in thermal capacity are realized. On the contrary, both nuclear and thermal production are flexible at the optimum level.