The attached PDF document includes the mathematical formulation for a day-ahead battery storage arbitrage model. This is exactly the model implemented in the online course "119" inside the Classroom (the full Python code is available to download). The battery owner uses a machine-learning model to forecast wholesale electricity prices over a 24-hour horizon. Then the battery owner employs either a linear programme or a mixed-integer linear programme to calculate a charging and discharging schedule designed to maximize expected profit. This optimization accounts for physical battery constraints including energy capacity, power ratings, symmetric round-trip efficiency losses, and state-of-charge dynamics. Once the day-ahead battery schedule is determined, the predicted battery profit is compared against the realized profit, which is calculated by applying the planned schedule to the actual prices. The difference between these figures represents a performance gap that measures the financial cost of errors in the initial price forecast. Full PDF is available below: