A city wants to build a new section of highway to link an existing bridge with an existing highway interchange, which lies 8 kilometers to the east and 10 kilometers to the south of the bridge. The first 6 kilometers south of the bridge is marshland. Assume that the highway costs $5 million per kilometer over marsh and $2 million per kilometer over dry land. The highway will be built in a straight line from the bridge to the edge of the marsh, then in a straight line to the existing interchange. At what point should the highway emerge from the marsh in order to minimize the total cost of the new highway? How much is saved over building the new highway in a straight line from the bridge to the interchange? (Hint: Use similar triangles to find the point on the boundary corresponding to a straight path and evaluate your cost function at that point.) The point is Bridge and we save S X S-X million. Marsh Interchange

A city wants to build a new section of highway to link an existing bridge with an existing highway interchange, which lies 8 kilometers to the east and 10 kilometers to the south of the bridge. The first 6 kilometers south of the bridge is marshland. Assume that the highway costs $5 million per kilometer over marsh and $2 million per kilometer over dry land. The highway will be built in a straight line from the bridge to the edge of the marsh, then in a straight line to the existing interchange. At what point should the highway emerge from the marsh in order to minimize the total cost of the new highway? How much is saved over building the new highway in a straight line from the bridge to the interchange? (Hint: Use similar triangles to find the point on the boundary corresponding to a straight path and evaluate your cost function at that point.) The point is Bridge and we save S X S-X million. Marsh Interchange

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 50A

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