A town on one island is to be supplied by electricity from a power plant on another island. The islands are 30 km apart and both are 2√3 km from the (same) shore of the main island. It costs Php 2 million per km to lay an underwater cable and Php 1 million per km to lay cables on the shoreline. To cut costs, the cable will run from the power plant to a point A on the shore, then along the shore from point A to point B, then from point B on the shore to the town. If the length of the underwater cables from the power plant to point A and from point B to the town are equal, how long should the cable be from point A to point B on the shore to minimize the cost of laying the cables? Assume that the shore of the main island is straight.
A town on one island is to be supplied by electricity from a power plant on another island. The islands are 30 km apart and both are 2√3 km from the (same) shore of the main island. It costs Php 2 million per km to lay an underwater cable and Php 1 million per km to lay cables on the shoreline. To cut costs, the cable will run from the power plant to a point A on the shore, then along the shore from point A to point B, then from point B on the shore to the town. If the length of the underwater cables from the power plant to point A and from point B to the town are equal, how long should the cable be from point A to point B on the shore to minimize the cost of laying the cables? Assume that the shore of the main island is straight.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A town on one island is to be supplied by electricity from a power plant on another island. The
islands are 30 km apart and both are 2√3 km from the (same) shore of the main island. It.
costs Php 2 million per km to lay an underwater cable and Php 1 million per km to lay cables
on the shoreline. To cut costs, the cable will run from the power plant to a point A on the
shore, then along the shore from point A to point B, then from point B on the shore to the
town. If the length of the underwater cables from the power plant to point A and from point B
to the town are equal, how long should the cable be from point A to point B on the shore
to minimize the cost of laying the cables? Assume that the shore of the main island is
straight.
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