Problem Solving with Extrema
This page describes real problems, both small and large, that
Extrema has been used to solve. From time to time we update it with
new problem-solving stories, to illustrate the wide range of difficult
problems that Extrema can tackle.
The Spread-Out Bragg Peak Problem
 The Problem: The radiation dose resulting from a proton passing
through living tissue has a sharp, narrow peak, known as a Bragg peak.
In certain cancer therapies, the desired radiation dose should have a
broad, flat peak, where the flat section corresponds to the extent of
the tumour being treated. The problem is how to deliver the dosage
in a broad, flat distribution when the radiation is naturally
deposited in narrow Bragg peaks.
Click here to see how this problem
was solved using Extrema.
The Waterpipes
Problem
The Problem:
We were given the job of figuring out the minimum amount of water
pipe necessary to connect up the houses on a street to a water main. We
had to determine where to dig a straight trench down the street for the
water main pipe. The houses are set back from the street by
varying distances, and ideally each house should be about 5 meters from the
water main. The problem was to find the trench that would result in the
minimum usage of water pipe segments from the main to the houses, and
the total length of the pipe needed.
Click here to see how this problem
was solved using Extrema.
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