Please take a look at the following word problem, it is from the Linear Programming section of my Math131 course:

A theatre is presenting a program on drinking and driving for students and parents. The proceeds will be donated to a alcohol information center. Admission is $2 for parents and $1 for students. There are two constraints; the theater can hold no more than 150 people, and every two parents must bring at least 1 student. How many parents and students should attend to raise the most money?

I know the answer is 100 parents and 50 students however I wasn't exactly sure how to put it in an algebric equation so I checked the solution manual which shows the following:

Let x = number of students

Let y = number of parents

x+y<=150 and 2x-y>=0

Answer is x+2y (100, 50) or 100 students and 50 parents.

I believe this to be wrong, that would equal $200. It should be the other way around! 100 parents and 50 students meets all the constraints and equals $250.

Can someone please confirm and give the correct formula(s). Wouldn't x+2y<=150 meet both constraints?

Thank you