Answer question 12 on pages 199200 of Winston*. Use GAMS to solve the necessary problems. Use "Binary Variables" to define binary decision variables. Give the formulation and clearly state which objective is being considered and which constraint is added at each stage of the process. 12 A small aerospace company is considering eight projects: Project 1 Develop an automated test facility. Project 2 Barcode all company inventory and machinery. Project 3 Introduce a CAD/CAM system. Project 4 Buy a new lathe and deburring system. Project 5 Institute FMS (flexible manufacturing system). Project 6 Install a LAN (local area network). Project 7 Develop AIS (artificial intelligence simulation). Project 8 Set up a TQM (total quality management) initiative. Each project has been rated on five attributes: return on investment (ROI), cost, productivity improvement, worker requirements, and degree of technological risk. These ratings are given in Table 67. The company has set the following five goals (listed in order of priority: Goal 1 Achieve a return on investment of at least $3,250. Goal 2 Limit cost to $1,300. Goal 3 Achieve a productivity improvement of at least 6. Goal 4 Limit manpower use to 108 . Goal 5 Limit technological risk to a total of 4. Use preemptive goal programming to determine which projects should be undertaken