Problema Solution
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 $4.00 for parents and$2.00 for students. However, this situation has two constraints: the theater can hold no more than 150 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 provided by our tutors
let
p = the number of parent
s = the number of students
the theater can hold no more than 150 people
s + p <= 150
every two parents must bring at least one student means
p/2 <= s
thus we have the following constrains
s + p <= 150
p/2 <= s
the objective function is the amount of money gathered
F(s, p) = 2s + 4p
first we need to fins the corner points of the graph of the system
s + p <= 150
p/2 <= s
click here to see the graph
the corner points are (0,0), (150, 0) and (50, 100)
F(0, 0) = 0
F(150, 0) = 2*150 = $300
F(50, 100) = 2*50 + 4*100 = $500
50 students and 100 parents should attend to raise maximum amount of money.