An oil refinery is located on the north shore of a river at point A in the diagram below. Theywish to lay a pipe to move their refined product to the railway yard, located on the south shore atpoint D, to get the oil to market. The river is 550 m wide (so the distance from point A to point Bis 550 m), and the railway yard is 1340 m downriver (so the distance from point B to point D is1340 m).It costs $1400 per m to lay pipe underwater, and $1000 per m to lay pipe over land.At what point C on the south shore of the river should they aim the underwater pipe in order tominimize the cost of the piping? Give your answer as the distance from point B.AriverBсTo solve this problem, you will apply the Closed Interval Method.The objective function, the function you want to minimize, is the cost. If we let I be the distancefrom point B to point C, thenC(x) =The closed interval over which you want to minimize this function is:x EDThe Closed Interval Method, an application of the Extreme Value Theorem, applies in this casebecause C(x) ison this closed interval.Find the critical point of C(x) in the interior of this interval.x =Evaluate C(x) atthe left endpoint: C =the critical point: C =the right endpoint: C =Based on the above, we may conclude that the distance from B to C that minimizes the cost ism

Answered: Image /qna-images/answer/3f6265fb-fcc4-48ee-8305-b5246f42f7a6.jpg

An oil refinery is located on the north shore of a river at point A in the diagram below. They wish to lay a pipe to move their refined product to the railway yard, located on the south shore at point D, to get the oil to market. The river is 550 m wide (so the distance from point A to point B is 550 m), and the railway yard is 1340 m downriver (so the distance from point B to point D is 1340 m). It costs $1400 per m to lay pipe underwater, and $1000 per m to lay pipe over land. At what point C on the south shore of the river should they aim the underwater pipe in order to minimize the cost of the piping? Give your answer as the distance from point B. A river B C To solve this problem, you will apply the Closed Interval Method. The objective function, the function you want to minimize, is the cost. If we let x be the distance from point B to point C, then C(x) = D

An oil refinery is located on the north shore of a river at point A in the diagram below. They wish to lay a pipe to move their refined product to the railway yard, located on the south shore at point D, to get the oil to market. The river is 550 m wide (so the distance from point A to point B is 550 m), and the railway yard is 1340 m downriver (so the distance from point B to point D is 1340 m). It costs $1400 per m to lay pipe underwater, and $1000 per m to lay pipe over land. At what point C on the south shore of the river should they aim the underwater pipe in order to minimize the cost of the piping? Give your answer as the distance from point B. A river B C To solve this problem, you will apply the Closed Interval Method. The objective function, the function you want to minimize, is the cost. If we let x be the distance from point B to point C, then C(x) = D

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.4: The Trapezoid

Problem 24E: The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340...

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