Refer to the transportation alternatives problem of Example 5.2. The bridge at Cay Road is actually part of the road between Augen and Burger. Therefore it is not reasonable for the bridge to have fewer lanes than the road itself. This means that if projects 2 or 4 are carried out, either projects 6 or 7 must also be carried out. Formulate a zero–one programming problem that includes this additional requirement. Solve the problem.

 

TABLE 5.2 TRANSPORTATION ALTERNATIVES Road between Augen and Burger 1 Concrete, 2 lanes 2 Concrete, 4 lanes 3 Asphalt, 2 lanes 4 Asphalt, 4 lanes Bridge at Cay Road Cost ($1,000) 2,000 3,000 1,500 2,200 5 Repair existing 6 Add lane 7 New structure Traffic Control in Downsberg 8 Traffic lights 9 Turn lanes 10 Underpass At most one project can be selected for each major objective. 500 1,500 2,500 100 600 1,000 NPV ($1,000) 4,000 5,000 3,000 4,300 1,000 1,500 2,500 300 1,000 2,000