= 1. An engineer is trying to choose a team of five workers to work on a project. The team consists of seven workers who have been rated (on a scale of 1 poor to 3 = excellent) according to their ability to conduct the project tasks (A, B, and C). The tasks that each worker is allowed to execute and the worker's skills (D, E, F, and G) are listed in Table 1. Table 1: Data for Problem 1 Tasks D A C Worker 1 2 3 4 5 6 7 A, B B, C A, B B, C A, B 3 2 2 1 3 3 3 E 3 1 3 3 3 1 2 F 1 3 2 3 3 2 2 HAVELIN G 3 2 The selected five-workers team must satisfy the following restrictions: a. At least 4 workers must be able to conduct task A, at least 2 workers must be able to conduct task B, and at least 1 worker must be able to conduct task C. The average level of each of the skills D, E, and F of the selected team must be at least 2. b. c. If worker 3 is included in the team, then worker 6 cannot be in the team. 2 1 3 3 1 d. If worker 1 is selected, then workers 4 and 5 must both be selected. e. Either worker 2 or worker 3 must be in the team. Given these constraints, the engineer wants to maximize the total value of ability G of the selected team. Formulate an IP that will help him choose his team. Solve the problem using CPLEX. (Hint: a binary variable in CPLEX can be defined as follows: "dvar boolean x 1;"). IN THE WHOLE 4

1. An engineer is trying to choose a team of five workers to work on a project. The team consists of seven workers who have been rated (on a scale of 1= poor to 3= excellent) according to their ability to conduct the project tasks ( A,B, and C ). The tasks that each worker is allowed to execute and the worker's skills (D, E, F, and G) are listed in Table 1. Table 1: Data for Prohlem 1 The selected five-workers team must satisfy the following restrictions: a. At least 4 workers must be able to conduct task A, at least 2 workers must be able to conduct task B, and at least I worker must be able to conduct task C. b. The average level of each of the skills D, E, and F of the selected team must be at least 2. c. If worker 3 is included in the team, then worker 6 cannot be in the team. d. If worker 1 is selected, then workers 4 and 5 must both be selected. c. Either worker 2 or worker 3 must be in the team. Given these constraints, the engineer wants to maximize the total value of ability G of the selected team. Formulate an IP that will help him choose his team. Solve the problem using CPLEX. (Hint: a binary variable in CPLEX can be defined as follows: "dvar boolean 1;" )