We went over exactly the same example last week in our Syntax class :D
I don't know how I could draw a tree here, but I can help you with the phrasal structures I think.
"The very small boy" is an NP because the head of the phrase is a noun: S-NP-D-The/NP-AP-AP-A-very/NP-AP-A-small/NP-N-boy,
"kissed the platypus" is a VP because the head is a verb: S-VP-V-kissed/VP-NP-D-the/VP-NP-N-platypus. I hope I was clear.
P.S.: Not a teacher nor a native speaker, just a Linguistics student.