10217

Lagrange's Milkmaid Problem

This Demonstration visualizes a classical example of constrained optimization using a Lagrange multiplier.
In the milkmaid problem [1], a milkmaid walks from her home at to the river at the point , draws a bucket of water, and brings it to the cow at . The problem seeks to minimize the total distance traveled, .
Use the slider to change the course of the river and drag the locators to change the positions of the maid and the cow. The red dashed arrows mark the path with minimal distance.
The curves of constant distance from to via a variable point are ellipses with and as focal points. At the point on the river where the distance is minimized, there must be a common tangent to the river and the ellipse of the minimal distance.

DETAILS

References
[1] S. Jensen. "An Introduction to Lagrange Multipliers." (2011) www.slimy.com/~steuard/teaching/tutorials/Lagrange.html.
[2] A. Segalla and S. Watson, "The Flip-Side of a Lagrange Multiplier Problem," The College Mathematics Journal, 36(3), 2005 pp. 232–235.

PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.