Question about solution for Coding Company

Problems and Contests
#1

Problem Statement: CSES - Coding Company
Solution: Solution - Coding Company (CSES) · USACO Guide

I think the “maximum possible unfinished team” is n and
“minimum possible value of total penalty” is -10000.

I think the dp array is dp[ max_n ][ 20000 ] but I can’t understand why dp array of all solution is just dp[ max_n/2 ][ 20000/2 ].

Can you explain why it worked?

#2

There are at most N/2 teams with more than one person.