1)The department has budgeted $700,000 to buy its 200 additional microcomputers, with delivery expected in the fall.
In this sentence does the phrase ''with delivery expected in the fall'' modife the verb '' buy'' or ''200 additional microcomputers''?
2)Customers who are less than three kilometers away can buy online with delivery to their home.
This is the another example . I thought that in this sentence modifies “buy”.
I don't think "with delivery" modifies anything in either sentence. It is additional information.
The department has budgeted $700,000 to buy its 200 additional microcomputers, with delivery expected in the fall.
This means: The department has set aside a certain amount of money and will buy the microcomputers with that money. Here is more information: Those microcomputers will be delivered in the fall.
Customers who are less than three kilometers away can buy online with delivery to their home.
This means: Customers within a certain distance can have their purchase delivered when they buy online. (Presumably customers who live farther away can still buy online, but they will have to arrange their own pick-up.)
To answer the question about sentence structure, yes, in both cases the phrases starting with "with delivery" are adverbial phrases, and in that sense "modify" the verb.
"With delivery expected in the fall" is an example of a special absolute construction that modifies a clause to give additional context. This construction is frequently discussed, e.g. here.
