A neighborhood child is selling lemonade and cookies in front of his house. He has up to 20 cookies available and enough lemonade for 50 glasses. The child makes a $1 profit off of each cookie and $0.50 profit off of each glass of lemonade and hopes to make at least $30.

Write a system of inequalities to represent the combination of the number of glasses of lemonade and cookies the child can sell.