You are here:

Calculus/math-calculus

Advertisement

Expert: - 11/11/2011


Question
Four cities are exactly located at the each end of square land with side 1mile. I want to connect four cities by roads in a manare that if is as inexpensive as possible. I am supposed to use optimal values. What can i do now?

Answer
I would draw an X with the roads, having a city at each of the four endpoints on the X.
The length of the two roads added together is √2 miles for each one.
Since there are two, this makes the total of both roads 2√2.

To do this properly, put the cities on a piece of graph paper at (0,0), (1,0), (0,1), and (1,1).
Put the point that all cities have a road to at some point (x.y) in the middle of the square with the cities.  The distance to the cities is
L(x,y) = √(x² + y²) + √((1-x)² + y²) + √(x² + (1-y)²) + √((1-x)² + (1-y)²).

Trying to take the derivative of that with respect to x or y seems rather complicated to me.
What I would do would be to put x=0.5, y=0.5 into the equation L(x,y) and get the answer.
Then see what L(x,y) gives at (0.49,0.5) and (0.51,5).
It will be found that L(x,y) increases to get to each of these values.
That same can be said about varying y, for x and y in the equation look the same.
In can then be seen the if more than one of the variables is varied, the solution is increased all the more.  From here, it can be said the maximum is at (0.5,0.5).

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2012 About.com, a part of The New York Times Company. All rights reserved.