Some entrepreneurs wish to establish a restaurant in a centrallocation so that it will serve three suburbs. On a rectangular gridwith axes labelled X1 (horizontal) and X2 (vertical), the centresof the three suburbs are located at (1,2), (6,18), and (12,8). All roads run east-west (parallel with the X1 axis) or north-south(parallel with the X2 axis). The distance between any two points istherefore rectilinear. For example, the distance between the centres of suburbs 2 and 3 is| 12 - 6 | + | 8 - 18 |= 6+10 = 16. Required:
a. Formulate the restaurant location problem as a goalprogramming model.
b. Use the Excel Solver to determine the best location for therestaurant.
c. Now suppose that suburb 1 is twice as large as suburb 2, andthree times as large as suburb 3. Write the new model, and solve itusing the Excel Solver.