1.) Scheduling and duration of a project. Suppose a project consists of 3 tasks each of 3 weeks long as follows.

Week Task 1 Task 2 Task 3 2 4 Constraints: C1. Every task is done exclusively by one engineer, it can not be done by two engineers (such as engineer 1 doing the first 2 weeks, and engineer 2 finishing the 3rd week) C2. An engineer can not work on more than one task in the same week. The same engineer can work on different tasks in different week (so engineer 1 can work on task 1 in week 2 and thein work on task 2 in week 3). We assume an engineer must be dedicated to one task in one week. . C3. Task 2 can not start until the first week of task 1 is complete. . C4. Task 3 can not start until the first week of task 2 is complete. C5. Common sense constraint: it is assumed that the third week of a task can not be done concurrently with week 2 (or week 1) of the task or before week 2 (or week 1) The table above is a scenario with 3 engineers doing 3 tasks that take a total of 5 weeks duration. The man-weeks cost of this project is 3 * 3-9 man-weeks (a) Suppose there is only one engineer working on this project. What is the minimum duration of the project now?. Explain! (b) What would be the duration with 2 engineers working on this? Explain! (c) Can this project be finished in less than 5 weeks with 4 or more engineers? Why? Suppose the (d) If we remove constraint C3 and C4 but keep C1, C2, and C5, can the project be finished in 5 (e) If we remove constraint C1, C3 and C4 but keep C2, and C5, can the project be finished in 5 constraints stated above are still true weeks with 2 engineers? Why? weeks with 2 engineers? Why? (f) An ambitious project manager wants to speed up the project and he / she has the hiring power of hiring 100 engineers on this project. With C1, C3, C4 removed but C2 and C5 stay, and with as many engineers as possible on this project, what is the minimum duration of this project? Why? Can this project be finished in 1 week