Agricultural landscapes provide many functions simultaneously including food production, regulation of water and regulation of greenhouse gases. Thus, it is challenging to make land management decisions, particularly transformative changes, that improve on one function without unintended consequences for other functions. To make informed decisions the trade-offs between different landscape functions must be considered. Here, we use a multi-objective optimization algorithm with a model of crop production that also simulates environmental effects such as nitrous oxide emissions to identify trade-off frontiers and associated possibilities for agricultural management. Trade-offs are identified in three soil types, using wheat production in the UK as an example, then the trade-off for combined management of the three soils is considered. The optimization algorithm identifies trade-offs between different objectives and allows them to be visualised. For example, we observed a highly non-linear trade-off between wheat yield and nitrous oxide emissions, illustrating where small changes might have a large impact. We used a cluster analysis to identify distinct management strategies with similar management actions and use these clusters to link the trade-off curves to possibilities for management. There were more possible strategies for achieving desirable environmental outcomes and remaining profitable when the management of different soil types was considered together. Interestingly, it was on the soil capable of the highest potential profit that lower profit strategies were identified as useful for combined management. Meanwhile, to maintain average profitability across the soils, it was necessary to maximise the profit from the soil with the lowest potential profit. These results are somewhat counterintuitive and so the range of strategies supplied by the model could be used to stimulate discussion amongst stakeholders. In particular, as some key objectives can be met in different ways, stakeholders could discuss the impact of these management strategies on other objectives not quantified by the model.