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hw-05-nlp - Math 319 Homework 5 Non-Linear Programming#1...

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Math 319 Homework 5: Non-Linear Programming #1: Facility Location Suppose we want to locate an airstrip somewhere in the desert where airplanes can land to drop off food aid, which will be trucked to various refugee camps. The camps are located and populated as follows: x y population 30 0 11 thousand people 300 20 20 thousand people 0 45 10 thousand people 60 60 13 thousand people The # of trips to each camp is proportional to the camp population. There are no roads for the trucks to use--they will drive straight from the airport to the camps. a) Formulate an NLP to minimize the total travel distance for the trucks (using math notation, not yet in Excel). b) Solve it using Excel. Hint: I get an objective function value around 6204.5 at optimality (not accounting for truck round trips). c) Is the optimal solution the same as the weighted average of the camps' locations? Compare both the location and the total cost. d) (optional) Does the optimal location change if you don't bother to take the square roots when computing the distances?
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