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A pipeline needs to be built to link two points A and B on either side of a river. B is 12km downstream of A. The project plans to lay the pipeline across the river to a point C and then follow the river on dry land to B as shown in the diagram below: C B. 200 m A . 12 km

A pipeline needs to be built to link two points A and B on either side of a river. B is 12km downstream of A. The project plans to lay the pipeline across the river to a point C and then follow the river on dry land to B as shown in the diagram below: C B. 200 m A . 12 km

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A pipeline needs to be built to link two points A and B on either side of a river. B is 12km downstream of A. The project plans to lay the pipeline across the river to a point C and then follow the river on dry land to B as shown in the diagram below: 1. C 200 m 12 km To cross the river a tunnel has to be built. It costs more to lay the pipeline under the river rather than on dry land. It costs £1.5 million per km to build the pipeline on dry land. The cost of building the pipeline through the tunnel is estimated to be 1.2 times the cost of building on dry land. Before making a decision on whether to go ahead with the project, it is necessary to determine the length of the tunnel that minimises cost. (i) Show that the cost (in millions of pounds) of the project is C = 1.8 Vx2 + 0.04 + 1.5 ( 12 – x ).
Transcribed Image Text:A pipeline needs to be built to link two points A and B on either side of a river. B is 12km downstream of A. The project plans to lay the pipeline across the river to a point C and then follow the river on dry land to B as shown in the diagram below: 1. C 200 m 12 km To cross the river a tunnel has to be built. It costs more to lay the pipeline under the river rather than on dry land. It costs £1.5 million per km to build the pipeline on dry land. The cost of building the pipeline through the tunnel is estimated to be 1.2 times the cost of building on dry land. Before making a decision on whether to go ahead with the project, it is necessary to determine the length of the tunnel that minimises cost. (i) Show that the cost (in millions of pounds) of the project is C = 1.8 Vx2 + 0.04 + 1.5 ( 12 – x ).
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