Question: A pipeline is being constructed to connect an existing location A to a new location B on the other side of a canal. The

A pipeline is being constructed to connect an existing location A to

A pipeline is being constructed to connect an existing location A to a new location B on the other side of a canal. The canal is straight and 1 km wide. Location B is 20 km downstream from location A but on the opposite side of the canal. The pipeline to connect the two locations will need to be laid partially in the canal and partially on land. The cost per kilometre to lay pipe in the canal is 25% more than the cost per kilometer to lay pipe on land. (a) Give the equation for total cost C(z) of laying the pipe to connect A to B where a is the length of pipe laid on the land (b) Determine the length of pipe laid in the canal that minimises the cost of laying the pipeline. (c) Mathematically show that your answer to (c) gives the (global) minimum in the cost.

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