Need help on a Calculus Problem
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Postmaster
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From: Sweetwater Texas
Need help on a Calculus Problem
I'm stumped on this one
An offshore well is located in the ocean at a point W, which is 5 miles from the closest shorepoint A on a straight shoreline. The oil is to be piped to a tank at Shorepoint B, that is 8 miles from A, by piping it on a straigh tline under water from W to some shorepoint P between A and B and hen on to B via a pipe along the shoreline. If the cost of laying pipe in $100,000 per mile under water and $75,000 per mile over land, where should the point P be located to minimize the cost of laying the pipe?
An offshore well is located in the ocean at a point W, which is 5 miles from the closest shorepoint A on a straight shoreline. The oil is to be piped to a tank at Shorepoint B, that is 8 miles from A, by piping it on a straigh tline under water from W to some shorepoint P between A and B and hen on to B via a pipe along the shoreline. If the cost of laying pipe in $100,000 per mile under water and $75,000 per mile over land, where should the point P be located to minimize the cost of laying the pipe?
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well its been a while but most places on the shoreline equal or exceed 950,000$, if there is a location that will be less than 950,000 it is between mile 7 to 8 ? For example at 7 miles away from point A on the shore its 8.7 miles aeay from W -cost is 945,000 at 7.5 miles away from A on the shore its 9.1 from W -cost is 947,000. Hope this helps.
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From: Tucker, GA
This is a trick question for three reasons:
1. See the "Entitlement" thread in this section. Accordingly, any answer is correct.
2. Eco-***** have stifled any offshore oil drilling, so the problem lacks relevance.
3. Whether you're on land or sea, laying pipe can cost you a lot of money. So be careful
1. See the "Entitlement" thread in this section. Accordingly, any answer is correct.
2. Eco-***** have stifled any offshore oil drilling, so the problem lacks relevance.
3. Whether you're on land or sea, laying pipe can cost you a lot of money. So be careful
Postmaster
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From: North of Boston MA
Six miles away from point A is where the pipeline should hit land, with two miles of onshore pipeline.
To do this you need two equations - one is the formula 100000X+75000Y which you want to minimixe. The other equation is the one for the right triangle with two variable sides. The one side is fixed at 5 miles and the other one ranges from 0 to 8 miles. So, your other equation is X=SQRT(5^2+(8-y)^2). Plug the equation above into the original equation, take the derivative and set it equal to zero and solve for X.
Or you could just do it in a spreadsheet and pick the smallest number like I did....
To do this you need two equations - one is the formula 100000X+75000Y which you want to minimixe. The other equation is the one for the right triangle with two variable sides. The one side is fixed at 5 miles and the other one ranges from 0 to 8 miles. So, your other equation is X=SQRT(5^2+(8-y)^2). Plug the equation above into the original equation, take the derivative and set it equal to zero and solve for X.
Or you could just do it in a spreadsheet and pick the smallest number like I did....
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From: North of Boston MA
Going straight from the well to the tank would be the hypotenuse of a right triangle with sides of 8 and 5 miles or 9.43 miles.
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Postmaster
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From: North of Boston MA
I wish the OP would chime in and let us know how we did.
Postmaster
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From: North of Boston MA
I finally sat down and did the problem out and came up with the following solution:
Point P should be 5.7 miles from point A, resulting in 7.58 miles of underwater pipe and 2.3 miles of on land pipe. Total cost comes to $930,722.
But, that is only $18,000 less than running the pipe completely underwater. You'd spend that much and then some operating and maintaining the pump station.
So, like was stated above - trick question.
Point P should be 5.7 miles from point A, resulting in 7.58 miles of underwater pipe and 2.3 miles of on land pipe. Total cost comes to $930,722.
But, that is only $18,000 less than running the pipe completely underwater. You'd spend that much and then some operating and maintaining the pump station.
So, like was stated above - trick question.
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Postmaster
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From: Sweetwater Texas
Sorry for takin so long to get back, been busy, Nitramjr is correct along with Jimmy Dean. You had to take a triangle, get one variable, take the derivative and set to zero. Thanks to Nitramjr and Jimmy Dean for helpin out
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