The cloud-based multi-agent system (MAS) results from the convergence of cloud computing and MAS, and the trustworthy data, the data that best matches the personalized demands of agents on trust attributes of data, is important for the cloud-based MAS. Data usage often comes with cost, and the better the trustworthiness of data (TOD), the higher the cost of data usage (CDU). Therefore, how to make the optimal trade-off for cloud-based MAS between TOD and CDU arises as an interesting issue. To address this issue, this paper proposes a mathematical constrained optimization model to help the agents to obtain the trustworthy data within the acceptable level of CDU. Experiments on a public dataset show its effectiveness.