Question

A theater is presenting a program on drinking and driving for students and their parents. The proceeds will be donated to a local alcohol information center. Admission is $18 for parents and $9 for students. However, this situation has two constraints: The theater can hold no more than 120 people and every two parents must bring at least one student. How many parents and students should attend to raise the maximum amount of money?

Answer 1

number of adults --- x
number of students ---y

condition#1: x+y ≤ 120
condition #2 : 2y ≥ x ----> y ≥ (1/2)x

Revenue equation:
R = 18x + 9y

I can "drag" this line out as far as the intersection of
y = (1/2)x and x+y = 120

then (1/2)x = 120-x
x = 240 - 2x
3x=240
x=80
then y = 120-80 = 40

so 80 parents and 40 students should attend for a max revenue of 18(80) + 9(40) or $1800