Maximum/Minimum - hints or pictures?

  • Thread starter Carl_M
  • Start date
  • Tags
    Pictures
In summary, the conversation discusses three different mathematical problems involving optimization. The first problem involves finding the outside dimensions of a billboard with a minimum total area given specific margins. The second problem involves finding the dimensions of a cylindrical soft drink can that minimize its cost, taking into account different costs for the sides, bottom, and top. The third problem involves determining the speed at which a bale of hay is rising when it is 2m below a loft, given the farmer's walking speed and the placement of a pulley. The conversation also mentions the need for equations and diagrams to solve these problems.
  • #1
Carl_M
13
0

Homework Statement


1. A billboard is to made with 100 m2 of printed area, with margins of 2m at the top and bottom, and 4m
on each side. Find the outside dimensions of the billboard if its total area is to be a minimum.


2. A cylindrical soft drink can is to have a volume of 500 ml. If the sides and bottom
are made from aluminum that costs 0.1¢/cm2, while the top is made from a thicker aluminum that costs 0.3
¢.cm2. Find the dimensions of the can that minimize its cost.


3. A farmer raises a bale of hay to a loft 6m above his shoulder by a 20 m rope using a pulley 1.5 m above
the loft. He walks away from the loft at 1.3 m/s. How fast is the bale rising when it is 2m below the loft?

What's the third one trying to say?

Homework Equations


Any pictures or diagrams by any chance?


The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Have you had a go at this?

First of all you need to find equations for your problems, and from there differentiate them to find the maximum/minimum.

If you have a go at the problems, I'll help you some more.
 
  • #3
In #3,

http://img405.imageshack.us/img405/4035/mmmcopy.png

Is this what it's saying for the diagram?
 
Last edited by a moderator:

FAQ: Maximum/Minimum - hints or pictures?

1. What is the difference between maximum and minimum values?

The maximum and minimum values represent the highest and lowest points, respectively, on a graph or in a data set. The maximum value is the largest value, while the minimum value is the smallest value.

2. How do I find the maximum or minimum value using a graph?

To find the maximum or minimum value using a graph, look for the highest or lowest point on the graph, respectively. You can also find the maximum or minimum value by finding the x-value where the slope of the graph changes from positive to negative or negative to positive.

3. How can I use calculus to find the maximum or minimum value?

To find the maximum or minimum value using calculus, take the derivative of the function and set it equal to zero. Then, solve for the x-value that makes the derivative equal to zero. This x-value represents the maximum or minimum value.

4. What are some real-life examples of finding maximum or minimum values?

Finding maximum or minimum values is commonly used in business and economics to determine the most profitable price point for a product. It is also used in engineering and science to optimize processes and designs.

5. Can maximum or minimum values be negative?

Yes, maximum and minimum values can be negative. This is especially true in situations where the data or function being analyzed can have negative values. It is important to consider the context and domain of the problem when interpreting the maximum or minimum value.

Similar threads

MHB MHB Introduces: Creating TikZ Pictures
Replies
1
Views
5K
B Does the Bernouli Effect Work On Cars?
Replies
8
Views
2K
Optimizing Cost for a Rectangular Box with Given Volume
Replies
1
Views
6K
LaTeX Help with page dimensions in latex
Replies
4
Views
2K
Engineering Stiffness of a Concrete Core in a Multi-Storey Building
Replies
2
Views
423
Mechanics of solids question from my mid semester exam
Replies
5
Views
4K
Calculating Loads for a 2m x 2m Concrete Tunnel with 4 Supports
Replies
4
Views
25K
Optimizing Area and Volume: Solving Maximum Problems
Replies
3
Views
6K
Solve Hard Fluid Problem: Calculate Minimum Work & Power of Pump
Replies
2
Views
8K
Max and Min Problems: Solving with Calculus | Need Help & Explanation
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top