Problem 1 (30 pts total) A small construction contractor has been asked to complete a variety of tasks for a particular construction project. Table 1 shows the six different tasks required and the number of rooms needing each particular task. For example, four rooms need electrical work. The contractor has four crew members: Beth, Dan, Jill and Peter. Hourly rates for each employee are shown in Table 2. Table 3 provides the length of time it takes each crew member to complete each task for a single room. You have been asked to construct a crew assignment model for the contractor to assign crew members to tasks in a minimal cost fashion. From the contractor's perspective, cost is measured in total wages spent on labor. Important considerations and restrictions for your model are below: A crew member can finish one room in the time noted in table 3. A crew member can be assigned to multiple rooms of the same task. Crew members cannot work more than 40 hours on this job. Crew members must each work at least 20 hours on this job. Dan and Jill have had bad experiences in the past working on fixtures collaboratively, therefore, both of them cannot be assigned to fixtures. Beth and Jill must work together on framing, if one of them is assigned to framing, the other must as well. To complete the job, all rooms must have the necessary tasks completed. Formulate the model as an integer program (using condensed mathematical notation), minimizing cost and ensuring all the restrictions are met. Write up your solution in lab report format. Solve the model using GAMS and provide your .gms and .lst (the portion showing the solution display) files as appendices to the report. Be sure to summarize the results within the body of the report, referencing the appendices. Table 1: Rooms requiring each task Task Rooms required Staging Framing 3 Electrical HVAC 3 Fixtures Finishing 3 Table 2: Hourly pay rate for each employee $/hr Crew member Beth Dan Peter Table 3: The number of hours required by each crew member to complete task for one room. Task Crew member Staging Framing Electrical HVAC Fixtures Finishing Beth 10 8 7 8 5 Dan 8 8 7 8 7 4 5 4 6 Peter 6 5 4 4 Problem 1 (30 pts total) A small construction contractor has been asked to complete a variety of tasks for a particular construction project. Table 1 shows the six different tasks required and the number of rooms needing each particular task. For example, four rooms need electrical work. The contractor has four crew members: Beth, Dan, Jill and Peter. Hourly rates for each employee are shown in Table 2. Table 3 provides the length of time it takes each crew member to complete each task for a single room. You have been asked to construct a crew assignment model for the contractor to assign crew members to tasks in a minimal cost fashion. From the contractor's perspective, cost is measured in total wages spent on labor. Important considerations and restrictions for your model are below: A crew member can finish one room in the time noted in table 3. A crew member can be assigned to multiple rooms of the same task. Crew members cannot work more than 40 hours on this job. Crew members must each work at least 20 hours on this job. Dan and Jill have had bad experiences in the past working on fixtures collaboratively, therefore, both of them cannot be assigned to fixtures. Beth and Jill must work together on framing, if one of them is assigned to framing, the other must as well. To complete the job, all rooms must have the necessary tasks completed. Formulate the model as an integer program (using condensed mathematical notation), minimizing cost and ensuring all the restrictions are met. Write up your solution in lab report format. Solve the model using GAMS and provide your .gms and .lst (the portion showing the solution display) files as appendices to the report. Be sure to summarize the results within the body of the report, referencing the appendices. Table 1: Rooms requiring each task Task Rooms required Staging Framing 3 Electrical HVAC 3 Fixtures Finishing 3 Table 2: Hourly pay rate for each employee $/hr Crew member Beth Dan Peter Table 3: The number of hours required by each crew member to complete task for one room. Task Crew member Staging Framing Electrical HVAC Fixtures Finishing Beth 10 8 7 8 5 Dan 8 8 7 8 7 4 5 4 6 Peter 6 5 4 4