If the heat pump is optimally sized, the time over which the backup resistive heater is used will be nonzero (assuming cost of the heat pump scales with its cap

If the heat pump is optimally sized, the time over which the backup resistive heater is used will be nonzero (assuming cost of the heat pump scales with its capacity). This is because spending extra to have it cover that last part is not worth it. This ignores its use for A/C; if in a place where the A/C load dominates the sizing then this argument doesn't apply.