NNs have emerged as a critical technology for edge intelligence. It is not possible to run large-scale NNs directly on Internet of Things (IoT) devices with limited energy since doing so requires a lot of resources and energy. By outsourcing certain NN layers to run on the edge server, NN partitioning offers a workable solution to this issue. Edge servers' resources, however, are often constrained. In such a realistic setting, it results in an resource and energy optimization-constrained problem.. Due to this, we look at an intractable nonlinear optimization issue known as NNoffloading and partitioning over a multiuser resource-constrained setting. We divide the issue into two smaller issues and provide an Energy-Management Neural Net Partitioning and Offloading (EMNPO) technique using dynamic programming and the theorem of minimum cut/maximum flow to find the solution in polynomial time. Lastly, we investigate how the energy limitation, NN type, and device count affect the effectiveness of the EMNPO. The technique suggested could dramatically improve the NN inference task's completion rate in comparison to other approaches as demonstrated by the simulation results of real NN models.