# How Do You Determine the Optimal Station Location Between Two Towns?

• asemh
In summary, the conversation is about finding the optimal location for a train station between two towns, A and B, that are 7km and 5km from a railroad line. The points C and D on the line are 8km apart, and the diagram provided shows that the optimal location for the station is between 0 and 8km. The goal is to minimize the length of the road from A to the station and then to B. The conversation also mentions setting up an equation L=f(S) and solving for S to find the optimal location.
asemh
Hi, I am having a hard time with this Optimization question as i do not know where to begin, I drew a diagram but what formulas, function etc do I use to start the question? And How do i do it?

Two towns A and B are 7km and 5km, respectively, from a railroad line. The points C and D nearest to A and B on the line are 8 km apart. Where should the station be located to minimize the length of a new road from A to S to B?

Here is the Diagram i drew:

http://img109.imageshack.us/img109/7071/diagramv.png

How would I start going about doing this problem?

Last edited by a moderator:
Can you write the length of the road as a function of where S is? (in particular, think of S as being the distance from point C)

See I can't tell if Point CS = 4km and point SD = 4km
I am not sure if they are both equivalent or not?
Im confused at this point.

I know the diagram is right because my teacher was helping me on that part.

I think you are trying to jump ahead. S (i.e. distance from C to the station as Office Shredder suggested) is the unknown. By the diagram you drew, the optimal value of S is somewhere between 0 and 8km. If you write an equation L = f(S) where L is the length of the road you are trying to minimize, then it's a matter of setting the derivative of L with repect to S equal to zero and solving for S.

## 1. What is optimization and why is it important?

Optimization is the process of finding the best solution to a problem, given a set of constraints and objectives. It is important because it allows for efficient use of resources and can lead to cost savings, increased productivity, and improved performance.

## 2. What are the different types of optimization?

There are several types of optimization, including linear programming, nonlinear programming, integer programming, and dynamic programming. Each type has its own specific approach and techniques.

## 3. How do you determine the optimal solution in an optimization problem?

The optimal solution is determined by considering all possible solutions and evaluating them based on the given constraints and objectives. This can be done mathematically using algorithms and optimization techniques.

## 4. What are some common applications of optimization in real-world scenarios?

Some common applications of optimization include supply chain management, scheduling and routing, financial planning, and resource allocation. It is also used in various industries such as transportation, manufacturing, and telecommunications.

## 5. How can optimization be used to improve decision-making?

By using optimization techniques, decision-making can be improved by considering all possible solutions and selecting the one that best meets the given objectives and constraints. This leads to more efficient and effective decision-making processes.

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