A demonstration agricultural microgrid containing solar photovoltaic (PV), battery storage system (BSS) and multiple water pumps and reservoirs is presented. A mathematical model of the cost of operating the demonstration microgrid is developed. The mathematical model includes hybrid inverter source switching and BSS charging modes in addition to power balance and inter-period energy and water-level coupling. Electricity pricing and irrigation water use efficiency are allowed to vary by time of day. The mathematical model is formulated as a mixed-integer linear program (MILP), implemented in Python using Pyomo, and optimized using the open-source SCIP solver to plan pumping and water usage. Estimated data for a demonstration system at a farm in Turkey is used to demonstrate the proposed model. Results of the optimization of the demonstration system show intuitive results that are superior to a rule-based initialization. The model may serve as the basis for model predictive control (MPC) or stochastic model predictive control (SMPC).