This is a problem #10, chapter 8 - Nonlinear Programming & Evolutionary Optimization, from the textbook by Cliff Ragsdale, "Spreadsheet Modeling and Decision Analysis".
This problem requires the use of Excel and the add-in, called Solver. The course is Excel-based and Solver is the optimization application used for all problems.
A traveler was stranded in her car recently in a snowy blizzard in Wyoming. Unable to drive any farther, the stranded motorist used her cell phone to dial 911 to call for help. Because the caller was unsure of her exact location, it was impossible for the emergency operator to dispatch a rescue squad. Rescue personnel brought in telecommunications experts who determined that the stranded motorist's cell phone call could be picked up by three different communications towers in the area. Based on the strength of the signal being received at each tower, they were able to estimate the distance from each tower to the caller's location. The following table summarized the location (X-Y coordinates) of each tower and the tower's estimated straight line (or Euclidean) distance to the caller.
See attached file for data.
The caller's cell phone battery is discharging quickly and it is unlikely the motorist will survive much longer in the subfreezing temperatures. However, the emergency operator has a copy of Excel on her computer and believe it might be possible, with your help, to use Solver to determine the approximate location of the stranded motorist.
(a) Formulate an NLP for this problem
(b) Implement your model in a spreadsheet and solve it.
(c) To approximately what location should the rescue personnel be dispatched to look for the motorist?
Excel file contains solution of nonlinearp programming problem using excel solver tool.