Route minimisation

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Route minimisation

Post by MathsTutor4You on Mon Sep 07, 2015 9:28 pm

The table shows the least times, in seconds, that it takes a robot to travel between six points in an automated warehouse. These six points are an entrance, A, and five storage bins, B, C, D, E and F. The robot will start at A, visit each bin, and return to A. The total time taken for the robot’s route is to be minimised.

(a) Show that there are two nearest neighbour routes that start from A. You must make the routes and their lengths clear.

(b) Starting by deleting F, and all of its arcs, find a lower bound for the time taken for the robot’s route.

(c) Use your results to write down the smallest interval which you are confident contains the optimal time for the robot’s route.

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