Case Study #1. Goal Programming A small Aerospace Company is considering 8 projects presented as follows: 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 TOM (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 below. The company has set the following five goals: Goal 1- Achieve a return on investment of at least $3,250. Goal 2- Limit cost to $1,300. Goal 3- Achieve a productivity improvement of at least 6. Goal 4- Limit man-power use to 108. Goal 5- Limit technological risk to a total of 4. Formulate a goal-programming model to determine which projects should be undertaken. First, develop the mathematical model of the given problem. Then, solve it using the Excel Solver program. Copy and Paste the Excel Solver Outputs to your solution. Clearly find and comment on values of the decision variables, deviational variables, and value of the objective function. Project 2 3 5 ROI ($) 2.070 456 670 350 495 380 1,500 480 Cost ($) 900 240 335 700 190 500 160 Productivity improvement 3 2 Manpower needed 18 18 27 36 6 18 24 Degree of risk 2 A N