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Math Help - Optimization problem I'm having trouble with

  1. #1
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    Optimization problem I'm having trouble with

    Optimization problem I'm having trouble with-math.png
    I have this optimization problem and I am not too sure how to proceed to solve it. So there is a continent y = (x+1)^2 +1 and an island (x^2)+(y^2)=1. We want to build a bridge that links the two functions at points (x1,y1) and (a,b). Here is what the problem is asking for:

    a) Formulate a question that consists of minimizing the cost, a problem without constraints of minimization of a degree 4 polynomial with 2 variable x1 and θ, so C(x1,θ) and formulate the conditions of first order.
    b) Knowing that the minimum for the cost is reached for
    θ=0.562371782 rad and x1=-0.68709
    determine the coordinates for the points P1=(x1,y1) and P2=(a,b)
    Last edited by Slyy23; December 2nd 2012 at 04:58 PM.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Optimization problem I'm having trouble with

    Whats the cost function. What exactly are we trying to minimize?
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  3. #3
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    Re: Optimization problem I'm having trouble with

    Quote Originally Posted by jakncoke View Post
    Whats the cost function. What exactly are we trying to minimize?
    They don't give me a cost function. They want me to formulate a way to minimize the cost for the construction of the bridge (so minimizing the distance between the continent and the island I guess). Also sorry if my problem is hard to understand, I am not in an English school and just tried my best to translate the problem.
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  4. #4
    Senior Member jakncoke's Avatar
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    Re: Optimization problem I'm having trouble with

    I'm not really understanding, you have a function  y = (x+1)^2 which has the point (0, 1), and (0,1) is also on the circle  x^2 + y^2 = 1
    They are already connected at point (0,1) ? So why do you need a bridge.
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  5. #5
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    Re: Optimization problem I'm having trouble with

    Sorry I wrote it wrong. It's y= (x+1)^2 +1
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