This preview shows pages 1–2. Sign up to view the full content.
Homework 1
IE418 – Discrete Optimization
Dr. Ralphs
Due January 30, 2007
1. A company has obtained permission to opencast mine within a square plot 200 ft X
200 ft. The angle of slip of the soil is such that it is not possible for the sides of
the excavation to be steeper than 45
◦
. The company has obtained estimates for the
value of the ore in various places at various depths. Bearing in mind the restrictions
imposed by the angle of slip, the company decides to consider the problem as one of
extracting rectangular blocks. Each block has horizontal dimensions 50 ft X 50 ft and
a vertical dimension of 25 ft. If the blocks are chosen to lie above one another, then
it is only possible to excavate blocks forming an upturned pyramid.
The following four diagrams show the percentage of pure metal in each of the blocks
within the maximum pyramid that can be extracted.
1.5
1.5
1.5
0.75
1.5
2.0
1.5
0.75
1.0
1.0
0.75
0.5
0.75
0.75
0.5
0.25
Level 1 (surface)
4.0
4.0
2.0
3.0
3.0
1.0
2.0
2.0
0.5
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Ralphs
 Optimization

Click to edit the document details