From a 480/277-volt, 3Ø, 4-wire panelboard, the maximum size DETD fuses that can be used on the motor branch circuit is:

The maximum size of DETD fuses allowed on a motor branch circuit is typically determined by the National Electrical Code (NEC), which outlines specific guidelines to ensure the safety and reliability of electrical installations, especially for motors.

In this scenario, the 480/277-volt, 3-phase, 4-wire panelboard indicates a standard industrial voltage for three-phase motors. When selecting the appropriate fuse size, one must consider the full-load current of the motor connected on that branch circuit. The NEC provides a formula which generally allows for a certain multiplier of the motor’s full-load current when determining the maximum fuse size.

For motors, the code often allows fusion protection at 125% of the motor's full-load current. However, this increase is capped at a particular maximum based on the ratings for fuses used in branch circuits feeding motors. In practical application, a circuit that typically has a maximum allowable fuse size may often be around 40 amps for motors and their associated overcurrent protection devices.

Thus, the answer reflects the ideal balance between both serving the motor's needs and adhering to code requirements. Hence, the appropriate maximum size DETD fuses for this motor branch circuit is correctly identified as 40 amps.