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ENGSCI 1036A/B (10)

Quazi Rahman (10)

Final

School

Western UniversityDepartment

Engineering ScienceCourse Code

ENGSCI 1036A/BProfessor

Quazi RahmanStudy Guide

FinalThis

**preview**shows half of the first page. to view the full**1 pages of the document.**5.5 Optimization Problems - Minimum Distance

1. A power line is to be constructed from the shore of a lake to an island that is 500m away. The closest

power line ends 4 km along the shore form the point on the shore closest to the island. If it costs 5 times

as much to lay the power line under water as along the shore, how should the line be installed to minimize

the cost?)

2. A man lives on an island 1 km from the mainland. His favourite pub is 3 km along the shore from the point

on the shore closest to the island. The man can paddle his canoe at 3 km/h and can jog at 5 km/h.

Determine where he should land so as to reach the pub in the shortest possible time.

3. A sailing ship is 25 km due north of a drifting derelict vessel. If the sailing ship sails south at 4 km/hs while

the derelict drifts east at 3 km/h, find the distance of closest approach of the two ships. (i.e. find the

distance between the two ships when that distance is a minimum)

Solutions

1.

64

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km from point closest to island, or 0.1 km 0â‰¤xâ‰¤4

2. 0.75 km, 0â‰¤xâ‰¤3

3. 15 km 0<t<6.25

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23. Lay pipe 465.4m along the shore from A, then lay the pipe from this point to B underwater

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