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anonymous
 5 years ago
An oil rig is to be built 30 miles down shore and 20 miles out to sea from a refinery. A pipe line needs to be built from the refinery to the oil rig. It costs $1000 per mile to build the pipe on land and $1500 per mile to build it at sea. The planners of this oil rig want to have the lowest cost possible for this pipe. How much would it cost to build the pipe line all the way down the shore until it is directly "below" the oil rig and then out to sea?
anonymous
 5 years ago
An oil rig is to be built 30 miles down shore and 20 miles out to sea from a refinery. A pipe line needs to be built from the refinery to the oil rig. It costs $1000 per mile to build the pipe on land and $1500 per mile to build it at sea. The planners of this oil rig want to have the lowest cost possible for this pipe. How much would it cost to build the pipe line all the way down the shore until it is directly "below" the oil rig and then out to sea?

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0are we assuming that the sea floor is flat?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this starts out to be a minimization problem but then the question asks something different. confusing.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010sqrt(13) * 1000 then

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the minimal distance between 2 points on a plane is a stright line

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its a pythag problem that has no real world application lol

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it seems to be asking; how much to build a pipeline along the legs of the triangle tho doesnt it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not to me but my reading comprehension might be off.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.01 if by land; 2 if by sea..... yeah, they want the minimal cost compared to yada yada yada

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but it doesn't ask for minimum cost, even though it says "The planners of this oil rig want to have the lowest cost possible for this pipe."

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is says "How much would it cost to build the pipe line all the way down the shore until it is directly "below" the oil rig and then out to sea? 8 minutes ago"

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we have to determine at what cost the land pipe and the sea pipe are qual

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, below being a pictorial term

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the shoreline is in a distance straight line from the refinery the oil rig is verticalto the shoreline and at angle between the shorline and refinery

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it looks to me as if it is just asking how much it would cost to build the pipeline 30 miles down the shore and then 20 miles out to sea. that is what the last statement says unless i am reading it incorrectly. is this for a calc class?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.025980.76 for a straight run to the oil rig

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0it is; but they want some variation of that;

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.030 miles down shore AND 20 miles out to sea from a refinery

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i take that to mean east 30 and then 20 north, for example. but of course i could be wrong.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.060000 if we build it at a right angle

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.052426.40 if we go with a 45 at 10 feet from the start

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0C(x) = s(1500) + l(1000)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0how to relate s an l? by angle perhaps?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sin(t) = l cos(t) = 30  cos(t) = s

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if this was speed; then the fastest speed would be?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i dont understand your question?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0straight shot; 54083.26 10 down and 45degrees gets us: 52426.40 11 down and a distance of sqrt(19^2 + 20^2): 52379.34 12(1000) + sqrt(18^2 + 20^2)(1500) = 52360.87

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its a matter if finding the route by land and by sea that is the cheapest to build

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.030(1000) + 20(1500) = 60 000 ; so just building it up the 30 then 20 is bad

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is sqrt supposed to mean log?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0log means log sqrt means square root

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what are you sqrting 11 down?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the pipeline goes along the beach; and each foot costs so much money ($1000) in that instance, we went down 11 feet and bent the pipe to go to the rig out at sea; the sea pipe costs 1500 per foot

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ideally, when the land pipe cost matches the sea pipe cost we have the cheapest cost

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when s(1500) = l(1000) we balance out and have the cheapest cost for total pipe

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0from the refinery to the oil rig would be the hypotenous of the other sides? multiplied to get the cost?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you soooooo very much for your help

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0can you get it from here?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i agree with amistre solution. however, since this is calc class you probably should (to make the teacher happy) have some sort of function to find the minimum of. so for the second part, and if you put "x" as suggested. then the distance from where the pipe enters the water to the oil rig is \[\sqrt{x^2+400}\] miles by pythagoras and the cost is $1500 per mile for a total of \[1500\sqrt{x^2+400}\] the distance from the refinery to where the pipe hits the water is 3\[30x\] miles at a cost of $1000 per mile for a cost of \[1000(30x)=300001000x\] and therefore your total cost will be \[C(x)=1500\sqrt{x^2+400}+300001000x\] this is the function you need to minimize

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[C'(x)=\frac{1500x}{\sqrt{x^2+400}}1000\] set = 0 to find the critical point get \[x=8\sqrt{5}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and don't forget that the distance down the shore line is not x, but rather 30x or about 12.11 rounded.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i did this on the fly so you should check my work. sure about the derivative though, and fairly positive about my \[x=8\sqrt{5}\]
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