This example illustrates non-preemptive goal programming.

Some entrepreneurs wish to establish a restaurant in a central location so that it will serve three suburbs. On a rectangular grid with axes labelled X1 (horizontal) and X2 (vertical), the centres of 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 is therefore rectilinear.

For example, the distance between the centres of suburbs 2 and 3 is | 12 - 6 | + | 8 - 18 |= 6+10 = 16.

(a) Formulate the restaurant location problem as a goal programming model.

(b) Use the Excel Solver to determine the best location for the restaurant.

(c) Now suppose that suburb 1 is twice as large as suburb 2, and three times as large as suburb 3. Write the new model, and solve it using the Excel Solver.