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Minimum Cost-Word Problem-Please Check?

  1. Jun 15, 2013 #1
    1. The problem statement, all variables and given/known data

    A gas pipeline is to be constructed from a storage tank to a house. A road runs straight from the tank, passing at its closest approach 300 feet away from the house at a point 600 feet away from the tank. Pipe laid along the road costs $8 per foot, while pipe laid off the road costs $10 per foot. What is the minimum cost for which the pipeline can be built?


    2. Relevant equations



    3. The attempt at a solution
    C= 8x + 10y

    [itex] y= √((600-x)^2 + 300^2)) [/itex]
    [itex] y= √(360000 - 1200x + x^2 + 90000) [/itex]
    [itex] y= √(450000 - 1200x + x^2) [/itex]

    [itex] y'= \frac {1}{2} (450000 - 1200x + x^2)^ \frac{-1}{2} [/itex]
    [itex] 8x + 10 (\frac {1}{2} (450000 - 1200x + x^2)^ \frac {-1}{2}) (-1200 + 2x)= 0 [/itex]
    [itex] -8= 5 (450000 - 1200x + x^2)^ \frac {-1}{2} (-1200 + 2x) [/itex]
    [itex] -8 (450000 - 1200x + x^2) \frac {1}{2}= 5 (-1200 + 2x) [/itex]
    [itex] -4 (450000 - 1200x + x^2) \frac {1}{2}= 5 (-600 + x) [/itex]
    [itex] 16 (450000 - 1200x + x^2) \frac {1}{2}= 25( x^2 - 1200x + 360000) [/itex]
    [itex] 9x^2 - 9x- 180000= 0 [/itex]
    [itex] x^2 - x - 200000= 0 [/itex]
    Just wondering, is it right so far? And if it is, how can I solve this quadratic without a calculator? :confused: Thanks!

    EDIT: I solved the problem again as the above method was wrong, and now I have it correct, but I just don't know how to delete posts so sorry for this waste of space on the boards >_<
     
    Last edited: Jun 15, 2013
  2. jcsd
  3. Jun 15, 2013 #2

    verty

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    Homework Helper

    You'll have to be much clearer about what you are doing at each step.
     
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