# Thread: Optimization problem I'm having trouble with

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

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
determine the coordinates for the points P1=(x1,y1) and P2=(a,b)

2. ## Re: Optimization problem I'm having trouble with

Whats the cost function. What exactly are we trying to minimize?

3. ## Re: Optimization problem I'm having trouble with

Originally Posted by jakncoke
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.

4. ## 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.

5. ## Re: Optimization problem I'm having trouble with

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