Oil from an offshore rig located 5 miles from the shoreline is to be pumped to a location on the edge of the shoreline that is 9 miles east of the rig. The cost of constructing a pipe in the ocean from the rig to the shore is 1.6 times as expensive as the cost of construction on land. Set up and analyze a model to determine how the pipe should be laid to minimize cost. Your "model" will need a clear drawing (or two or three or more) that shows different ways that the pipe can be laid. You will also need to explain the drawing and the parts of it that are subject to optimization. One of your drawings needs to give the arrangement that minimizes cost (with measurements and total cost included). You also need to give written mathematical proof/reasoning why this arrangement minimizes cost. Yes, your reasoning should definitely involve calculus and derivatives!
Oil from an offshore rig located 5 miles from the shoreline is to be pumped to a location on the edge of the shoreline that is 9 miles east of the rig. The cost of constructing a pipe in the ocean from the rig to the shore is 1.6 times as expensive as the cost of construction on land.
Set up and analyze a model to determine how the pipe should be laid to minimize cost.
Your "model" will need a clear drawing (or two or three or more) that shows different ways that the pipe can be laid. You will also need to explain the drawing and the parts of it that are subject to optimization.
One of your drawings needs to give the arrangement that minimizes cost (with measurements and total cost included). You also need to give written mathematical proof/reasoning why this arrangement minimizes cost. Yes, your reasoning should definitely involve calculus and derivatives!
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