# Maximizing xy^2

Pro Problems > Math > Calculus > Differential > Max and Min## Maximizing xy^2

x and y add to 12. Find x so that the product xy^{2} is maximized on the interval 0 < x < 12

## Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### Melting a Golden Cube

1 cubic foot of gold is melted down and molded into a cylinder. If the cylinder is to have the minimum possible surface area, what will the cylinder’s radius be?

### Height of Launch

h(t) = 150 + 400t - 16.1t^{2}

What is the maximum height the rocket attains before it begins to fall to the earth?

### Two Big Pig Pens

Farmer Jones has 3000 feet of fencing material. He wants to use this fencing material to create two rectangular pig pens that share a common side, and such that one of the pens is twice the area as the other. He wants to maximize his area. What dimensions should he use for the two pig pens?

### Quadratic Maximum

A quadratic function has a maximum at (1,5,2.5), and crosses the y-axis at y = -2. Find the function.

### Cost of a Can

A can is required to have a volume of 150p cubic centimeters. The cost of producing the top and bottom is $0.001 per square cm, and the cost of producing the side is $0.0008 per square cm. What will be the radius of the can which meets the volume criteria, but costs the least to produce? What will be the price of producing this can?

### Paint and Framing

^{2}customers in the store each day, with each customer purchasing (on average) 3 tubes of paint. Of those customers,

# Ask Professor Puzzler

Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!**Get a**

*FREE*Pro-Membership!Educators can get a free membership simply by sharing an original lesson plan on our

*Articles for Educators*page!