Maximum/Minimum - hints or pictures?

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SUMMARY

The discussion focuses on solving optimization problems involving a billboard, a cylindrical can, and a pulley system. The first problem requires determining the dimensions of a billboard with a fixed area of 100 m² while accounting for specified margins. The second problem involves minimizing the cost of materials for a cylindrical can with a volume of 500 ml, where different costs apply to the top and sides. The third problem addresses the rate at which a bale of hay rises as a farmer walks away from a loft, requiring an understanding of related rates and geometry.

PREREQUISITES
  • Understanding of calculus, specifically differentiation for optimization
  • Familiarity with geometric formulas for area and volume
  • Knowledge of related rates in physics
  • Basic algebra for solving equations
NEXT STEPS
  • Study optimization techniques in calculus, focusing on finding maximum and minimum values
  • Learn about geometric properties of cylinders and their surface area calculations
  • Explore related rates problems in calculus to understand dynamic changes
  • Review cost minimization strategies in real-world applications
USEFUL FOR

Students studying calculus, particularly those focusing on optimization problems, as well as educators seeking to enhance their teaching methods in applied mathematics.

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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
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.
 
In #3,

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

Is this what it's saying for the diagram?
 
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