# Maximum/Minimum - hints or pictures?

• Carl_M
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.

## 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

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 [Broken]

Is this what it's saying for the diagram?

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