Problem Statement - Selecting Projects for Bidding: A contractor has identified a set of eight major construction projects that are to be awarded on the basis of sealed bids. The contractor is reasonably confident of being able to submit the low bid on each of the projects, but does not have the resources to undertake all of them. The projects are large in scale, and each will require different levels of labor, materials, and equipment to complete. The contractor's labor and equipment resources are limited. Each bid also requires time and special expertise to prepare, and these are limited as well. The question facing the contractor is which projects should be selected for bidding. The relevant data for each of the eight projects are presented in Table 1, including the time necessary to prepare a bid and the expected profit that would result from being awarded and completing each project. Estimates for the major resources needed for a particular project are also included. For example, project 3, the re- decking of an urban bridge crossing a major river would require a skilled labor input of about 4,000 hours and the use of a very large crane during almost the entire project. The bid for this project would be the first of its kind undertaken by this contractor, and would thus take approximately 13 person weeks to prepare. The profit resulting from being awarded and successfully completing this project is estimated to be $100,000. The resources available to the contractor for preparing bids and completing projects that might be awarded are limited. The company owns three cranes, each of which is suitable for any of the projects. Only 30,000 hours of skilled labor are expected to be available to the contractor during the period of the projects. A team of four project estimators will prepare all bids so that over the next three months, a total of only 50 person-weeks is available. Also, due to the distance between projects, project number 7 and number 8 cannot be jointly pursued. The company confidently assumes that it will win any bid that it prepares. Which projects should be pursued? 1. (35 points) Formulate the model using the five elements of a math program maximizing profit and adhering to the constraints described in the problem description above. 2. (15 points) Describe the method you would use to solve this model. Detail (but do not solve) the basic steps associated with the method and how they would relate to the problem given. For example, would you use the graphical method, simplex method, or branch and bound? 3. (10 points) Formulate and solve your model using GAMS. Provide a copy of the .gms and .Ist files in your submission. Table 1: Project Requirement Data Time to prepare Project # bid (person-weeks) Thousands of hours of skilled labor needed 6 5 Crane Required? (1 = yes, 0 = no) Profit if Project Won ($1000) 1 0 1 2 3 4 5 8 12 13 11 9 4 1 0 7 8 80 110 100 90 70 80 90 60 0 w 00 6 7 3 1 7 8 4 1 0 00 8 8 5 1