A major city in the northeast wants to establish a central transportation station from which visitors can ride buses to four historic landmarks. The city is arranged in a grid, or block, structure with equally spaced streets running north and south and equally spaced avenues running east and west. The coordinates of any corner of any block in the city can be identified by the street and avenue numbers intersecting at that particular corner. The following table gives the coordinates for the four historic landmarks:

The transportation planners want to build the transportation station at the location in the city that minimizes the total travel distance (measured rectangularly) to each landmark. For example, if they built the station at 6th Street and 2nd Avenue, the total distance to each landmark will be:

a. Plot the locations of the various historical landmarks on a graph where the X-axis represents avenue numbers (starting at 0) and the Y-axis represents street numbers (starting at 0).
b. Formulate an LP model to determine the corner at which the central transportation station should be located. (Let the decision variables represent the street location (X1) and avenue location (X2) of the station and use deviational variables to measure the absolute street distance and absolute avenue distance from each landmark to X1 and X2. Minimize the sum of the deviationalvariables.)

Transcribed Image Text:

Landmark Street Avenue Landmark Distance 2 3 4 7-6 13-21 11-2 13-61 11-2 314 1-6 16-2 54 9 6-6 19-2 07-7 Total Distance 22