This is a non-standard, but fun and interesting optimization problem.
While standing on the shore, given top running and swimming speeds and the location of a struggling swimmer in x and y coordinates, the lifeguard must decide how far to run before diving in the water. While running is faster, it also increases the total distance that must be covered.
This problem serves as a vehicle with which to demonstrate how to use Microsoft Excel to solve optimization problems and do comparative statics analysis.
The Comparative Statics Wizard is an Excel add-in that walks the user through a series of steps in order to conduct comparative statics analysis. The files below use the Comparative Statics Wizard. The lifeguard problem is used as an example. The Comparative Statics Wizard is extremely flexible -- any problem solved by Excel's Solver can be run through the Wizard to get comparative statics analyses.
Click on the links below to download any of the Excel or Word files. The file should automatically launch Excel or Word which then opens the file, but you may have to open the file manually. If your browser opens the file WITHIN the browser (as a plug-in), go back and right-click to download the file to your hard drive.
The Excel files contain macros and you should click Enable Macros when prompted in order to properly work with the files.
You will need Word97 and Excel97 or greater in order to use these materials. Windows or MacOS can be used.
The Comparative Statics Wizard add-in must be properly installed. For complete instructions on downloading and installing the Comparative Statics Wizard add-in, please go to www.wabash.edu/econexcel/compstatics/download.
Lifeguard.doc -- a Word file that explains all of the Word and Excel materials on this site. It contains a discussion of the merits and uses of the Comaparative Statics Wizard add-in.
LifeguardIntro.xls -- an Excel workbook that describes the problem and solves it via traditional methods.
LifeguardSolver.xls -- illustrates the use of Excel's Solver to find the initial optimal solution and is used to demonstrate the Comparative Statics Wizard add-in.
Solver.doc -- a guide to the installation and use of Excel's Solver.
LifeguardConOpt.xls -- uses the LaGrangean Multiplier Method to solve a constrained optimization version of the lifeguard problem
LifeguardGame.xls -- be a lifeguard and decide when to enter the water! Are you optimizing?
Humberto Barreto
Department of Economics
Wabash College
Crawfordsville, IN 47933
Email: barretoh@wabash.edu
Phone: 765.361.6315
FAX: 765.361.6277
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