Please do it by hand

2. (The road ) 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. Example 5.2 (County transportation choices) Suppose that the goals and spe- cific projects shown in Table 5.2 are being considered by the County Transportation Authority. Chapter 5 APPLIED INTEREST RATE ANALYSIS TABLE 5.2 TRANSPORTATION ALTERNATIVES Cost ($1,000) NPV ($1,000) 2,000 3,000 1,500 2,200 4,000 5,000 3,000 4,300 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 5 Repair existing 6 Add lane 7 New structure Traffic Control in Downsberg 8 Traffic lights 9 Turn lanes 10 Underpass 500 1,500 2,500 1,000 1,500 2,500 100 600 1,000 300 1,000 2,000 At most one project can be selected for each major objective. There are three independent goals and a total of 10 projects. Table 5.2 shows the cost and the net present value (after the cost has been deducted) for each of the projects. The total available budget is $5 million. To formulate this problem we intro- duce a zero-one variable for each project. (However, for simplicity we index these variables consecutively from 1 through 10, rather than using the double indexing pro- cedure of the general formulation presented earlier.) The problem formulation can be expressed as maximize 4x + 5x2 + 3x3 + 4.3x4 + x3 +1.5x6 +2.5x7 +.3x3 + x9 + 2x10 subject to 2x1 +3x2 + 1.5x3 +2.2x4 +.5x5 +1.5x6 +2.5x7 +.1x8 +.6x9 +x1055 x1 + x2 + x3 + x4