Question

A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is

$ 2.00$2.00

for adults and

$ 1.00$1.00

for students.​ However, this situation has two​ constraints: The theater can hold no more than

150150

people and for every two​ adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of​ money?

Answer 1

Let ,

x = number of students in attendance

y = number of adults in attendance

we want to maximize the following objective function

for the constraints ,

drawing the graph for the inequalities we get ,

we get three vertex for the common region of inequalities ,

we find the value of objective function at each vertex of the graphed region .

At (0,0) :

At (50,100) :

At (150,0) :

we find the point where the objective function is maximized , that is $250 .

The maximum amount of money is raised ($250) when 50 students and 100 adults are in attendance