The bicycle problem involves n people who have to travel a distance of 20km, and

Question

The bicycle problem involves n people who have to travel a distance of 20km, and have one single-seat bicycle at their disposal. The data are specified by the walking speed Wj and the bicycling speed bj of each person person j, (j = 1,..., n). The task is to minimize the arrival time of the last person. The following LP is used to fulfill the task: min t s, t, t ... xj ... x'j ... yj ... y'j 0 (1 j n) t - nj=1 yj - nj=1 y'j o WjXj - WjX'j + bjyj - bjy'j = 20 (1 j n) nj=1 bjyj - nj=1 bjy'j 20 xj, xj, yj,y'j 0 (1 j n) Interprete the variables and the constraints. Why does the optimal value of the LP provide a lower bound on the optimal value of the bicycle problem. Why is the optimal value of the LP only a lower bound? Construct an example for which the optimal value of the LP is strictly less than the minimal arrival time of the last person. Find an optimal solution to the bicycle problem with n = 3 and the following data:

Explanation / Answer

u r not allowed to ask so many questions in a single post pls split them in multiple post n ask again(i know that they r interrelated) so post one part get tthat solution n then post the other part thanks

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