Investigation The retail outlets described in Exercise 22

Chapter 13, Problem 23

(choose chapter or problem)

Investigation The retail outlets described in Exercise 22 are located at and (see figure). The location of the distribution center is and therefore the sum of the distances is a function of and (a) Write the expression giving the sum of the distances Use a computer algebra system to graph Does the surface have a minimum? (b) Use a computer algebra system to obtain and Observe that solving the system and is very difficult. So, approximate the location of the distribution center. (c) An initial estimate of the critical point is Calculate with components and What direction is given by the vector (d) The second estimate of the critical point is If these coordinates are substituted into then becomes a function of the single variable Find the value of that minimizes Use this value of to estimate (e) Complete two more iterations of the process in part (d) to obtain For this location of the distribution center, what is the sum of the distances to the retail outlets? (f) Explain why was used to approximate the minimum value of In what types of problems would you use Sx, y?