optimization: minimize cost of piping water from 1 pt on river to 2 towns

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mika0

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10. You have been asked to determine where a water-works should be built along a river, between Chesterville and Denton, to minimize the total cost of the pipe to the towns.
(a) Assume that the same size (and cost) pipe is used to each town. (This part can be done quickly without using calculus.)
(b) Assume that the pipe to Chesterville costs $3,000 per mile, and to Denton it costs $7,000 per mile.

is there anyone who can help me to solve this exercise?
 

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mika0 said:
10. You have been asked to determine where a water-works should be built along a river, between Chesterville and Denton, to minimize the total cost of the pipe to the towns.
(a) Assume that the same size (and cost) pipe is used to each town. (This part can be done quickly without using calculus.)
(b) Assume that the pipe to Chesterville costs $3,000 per mile, and to Denton it costs $7,000 per mile.

is there anyone who can help me to solve this exercise?
Click to expand...

Of course there are many of us ready to help you?

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting
 
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To tell the truth I don't have any thoughts,I don't know how to start from where for solving it
 
mika0 said:
To tell the truth I don't have any thoughts,I don't know how to start from where for solving it
Click to expand...
You have two right triangles where the amount of pipe needed is the hypotenuses. You are given the legs of the triangles; one of 3 and x and the other of 5 and 10-x. So compute the hypotenuses and multiply by the respective cost for each section of pipe. Add the two together to get a final total cost function and find the minimum of the function within the given constraints [0<x<10].
 
mika0 said:
To tell the truth I don't have any thoughts,I don't know how to start from where for solving it
Click to expand...
This is deeply disturbing. They've given you the picture; they've defined a variable; they've given you a question (in part (a) of the exercise) which they point out does not necessarily require calculus. So your inability even to guess where to get started suggests that you didn't take algebra (at least not any year recently), and don't know about things like the Pythagorean Theorem. If this is true, then you need to have a serious talk with your academic advisor about appropriate course placement.

In hopes, on the other hand, that you were exaggerating:

You are given a picture:

Code: 
piping:
                  D
C                '|
| '            '  |
|3   '       '   5|
|       '  '      |
L---------P-------R
|<---x--->|
|<-------10------>|

The river is an horizontal line across the bottom. Town C is 3 units up a vertical perpendicular line from the left-hand end of the portion of the "river" line; Town D is 5 units up a vertical perpendicular from the right-hand end of the line. The distance between the feet of these perpendiculars is given as being 10 units; the point on the line to which each of C and D is to be joined is given as being "x" units from the left-hand end.

So you have two right triangles. Labelled the river-line endpoints and L and R (for "left" and "right") and the piping point as P, we have triangles LCP and RDP. Applying the Pythagorean Theorem, what expressions can you create for the lengths of CP and DP? ;)
 
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