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Formulate a lp model-the project manager

**Assignment:**

Q: A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) Total 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees. Please use GAMS to find the optimal solution and optimal value.

Projects |
A |
B |
C |

Maximum Number of Employees |
5 |
6 |
3 |

Reduction of Completion Time (days / employee) |
3 |
9 |
3 |

Expected delivery within 24 Hours

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