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 $14.00 for adults and $7.00 for students.​ However, this situation has two​ constraints: The theater can hold no more than 240 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?

Question
Asked Jun 11, 2019
263 views

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 $14.00 for adults and $7.00 for students.​ However, this situation has two​ constraints: The theater can hold no more than 240 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?

check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

Let x= number of adults 

Let y= number of parents 

To maximize the revenue Z=14x+7y,

Subject to a contraints 

x+y<=240,

x/2<=y,

restrictions are x<=0, y<=0.

Step 2

Graph these 4 inequalities with x on the x-axis and y on th y-axis.

In the graph the common solution of the 4 inequalities form a triangle in the first quadrant with one vertex at the origin (0,0), second vertex at(0,240), and third vertex  y=240-x, and  y=x/2

(3/2)*x=240,

x=160, and y=80.

So, the third vertex is (160,80).

help_outline

Image Transcriptionclose

300 (0, 240) 200 -100 (160, 80) (0, 0) 00 200 30 -100 -200

fullscreen
Step 3

The extrema (maximum and minimum ) of the revenue function will occur at the vetrices of the triangle, 

So, plug those values into the r...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Differential equations Consider the vectors x1(t) and x2(t) Please refer to attached image for vecto...

A: Obtain the Wronskian of the vectors as follows.

question_answer

Q: Consider the following sets. The universal set U for this problem is the set of all residents in Ind...

A: a.) Consider the universal set U as the set of all residents of India which contains the set of Engl...

question_answer

Q: 2. Prove that if n is even, then 3n + 1 is odd

A: The given expression is 3n + 1. Prove that 3n + 1 is odd, if n is even.

question_answer

Q: A clothing retailer gives you 10 points for every $1 spent, and you can trade in 2,550 points for a ...

A: The formula to find cost of each item is E3=D3×C3.Thus, the  cost of 3 polo shirt is $ 150.00.Here f...

question_answer

Q: I need help for number 4. Thanks!

A: We need to show that

question_answer

Q: Abstract Algebra. Please explain everything in detail.

A: To discuss the reason why the three given functions fail to satisfy the properties of a Euclidean no...

question_answer

Q: Hello I am having trouble understanding Set Theory and Subsets.

A: Set theory is dealing with objects that are related to the mathematics and it is also a branch of ma...

question_answer

Q: prove in a field with four elements, F = {0,1,a,b}, that 1 + 1 = 0.

A: The given four elements are F = {0, 1, a, b}.Consider ab belongs to F and then there are four possib...

question_answer

Q: Pls explain to me step by step and write clearly. Thanks a lot

A: Rewrite the given nonlinear two dimensional system as follows. x’ = x + y–x (x2 + y2 ) and y’ = – x ...