Applied Optimization Suggestions

[turdferguson]

For a calc project, I am supposed to solve an interesting calculus word problem dealing with maximum and minimum values. The catch is that I cannot use my own book. Can anyone suggest a challenging optimization problem? So far, we've covered the problem with a person who must find the least time required to get from A to B across a river if he can run on land faster than he can swim in water. I can also rule out the pipe around a corner problem, Fermats Principle, and Snells Law. If anyone has encountered an interesting, out of the ordinary max/min problem (single variable), please help me out

 

[kuahji]

A street light is mounted at the top of a 15ft tall pole. A man 6ft talk walks away from the pole with a speed of 5ft/sec along a straight path. How fast is the tip of his shadow moving when he is 40ft from the pole?

Its a pretty interesting problem that you also have to use a bit of trig/geometry to solve.

 

[turdferguson]

That is more of a related rates question. I could solve for the minimum/maximm speed of the shadow, but we've dealt with that basic setup already

 

[kuahji]

oops :), yeah you're right, wasn't really paying attention. Ok, how about

A rain gutter is to be constructed from sheet metal with width 30cm by bending up one-third of the sheet on each side through an angle theta. How should theta be chosen so that the rain gutter will carry the maximum amount of water (maximum cross-sectional area)?

 

[turdferguson]

Thats a good one (with nice geometer's sketchpad potential), but someone else is already doing it. So far, I've found this:

Two poles, one 6 meters tall and one 15 meters tall, are 20 meters apart. A length of wire is attached to the top of each pole and it is also staked to the ground somewhere between the two poles. Where should the wire be staked so that the minimum amount of wire is used?