Exercise 9.77 Consider the situation as depicted on the following simplified map. Mountain River 20 km 2 km 1 km B A road from locations A to B has to be constructed. The first part of the road from A to P requires building a tunnel through a mountain. Then, for the part from P to Q, a bridge over a river has to be built. The final part from Q to B can follow the riverside. Obviously, the unit costs for these three construction types differ. A tunnel costs €15 million per km, while a bridge costs €10 million per km and, finally, the road along the riverside €5 million per km. Position the intermediate locations P and Q such that the total costs of construction are minimized.
Exercise 9.77 Consider the situation as depicted on the following simplified map. Mountain River 20 km 2 km 1 km B A road from locations A to B has to be constructed. The first part of the road from A to P requires building a tunnel through a mountain. Then, for the part from P to Q, a bridge over a river has to be built. The final part from Q to B can follow the riverside. Obviously, the unit costs for these three construction types differ. A tunnel costs €15 million per km, while a bridge costs €10 million per km and, finally, the road along the riverside €5 million per km. Position the intermediate locations P and Q such that the total costs of construction are minimized.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:Exercise 9.77 Consider the situation as depicted on the following simplified map.
P
Mountain
River
20 km
2 km
1 km
B
X
A road from locations A to B has to be constructed. The first part of the road from A to P
requires building a tunnel through a mountain. Then, for the part from P to Q, a bridge
over a river has to be built. The final part from Q to B can follow the riverside. Obviously,
the unit costs for these three construction types differ. A tunnel costs €15 million per
km, while a bridge costs €10 million per km and, finally, the road along the riverside €5
million per km. Position the intermediate locations P and Q such that the total costs of
construction are minimized.
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