Problema Solution
A theater is presenting a program for students and their parents on drinking and driving. The proceeds will be donated to a local alcohol center: Admission is $10.00 for parents and $5.00 for students. However, the situation has 2 constraints. The theater can hold no more than 210 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
x = the number of parents, x>=0
y = the number of students, y>=o
The constrains can be described with the following inequalities:
x + y <= 210
x <= 2y
The objective function is F(x, y) = 10x + 5y. We need to find the maximum for F(x, y).
First, we need to find the corner points - click here to see the graph :
The corner points are (0, 0), (140, 70), (0, 210).
Next we calculate the objective function in the corner points:
F(0, 0) = 0
F(140, 70) = 10*140 + 5*70 = $1,750
F(0, 210) = 5*210 = $1,050
To rise maximum amount of money, 140 parents and 70 students should attend.