Duty of a Shudra is not giving alms to Brahmins, as they are prohibited from having wealth.
Mahabharata Santi Parva chapter 59:
A Sudra should never amass wealth, lest, by his wealth, he makes the members of the three superior classes obedient to him. By this he would incur sin. A Sudra cannot have any wealth that is his own.
A Brahmana may confidently seize the goods of (his) Sudra (slave); for, as that (slave) can have no property, his master may take his possessions.
No collection of wealth must be made by a Sudra, even though he be able (to do it); for a Sudra who has acquired wealth, gives pain to Brahmanas.
So, Serving the other three castes by money cannot be done by Shudra, as he is not allowed to have wealth.
The Brahmana who takes his food in the company of Sudras is purged from all impurity by duly observing the ceremonies of purification. (Actually Brahmins are not even allowed to eat food of other Brahmins)
Another duty of the Brahmana consists in avoiding the food prepared by the Sudra.
So, offering food to other three castes is not the duty of Shudra, as it is also prohibited.
Then, what is the duty of Shudra? In what way he can serve others?