Objective: To solve the provided project management problems, showing all calculation steps clearly and presenting the final answers in a professional manner.Problem 1Courter Corporation is developing a new speaker system (Gina3000) and has identified a set of 10 project activities with dependencies and estimated durations. You are provided with the following simplified activity list:Activity A: 2 weeks (no predecessor)Activity B: 3 weeks (no predecessor)Activity C: 4 weeks (A)Activity D: 1 week (B)Activity E: 2 weeks (C)Activity F: 3 weeks (D, E)Using this information:Question:1. Construct a network diagram for the above activities.2. Identify the critical path and calculate the project completion time.3. Determine the earliest and latest start and finish times for each activity.4. Which activities have slack time? What does this imply for project scheduling?Problem 2A software development firm is running behind schedule on a 20-week project and needs to reduce the total duration to 17 weeks. The following activities are on the critical path and can be crashed:Activity \(\mathrm{X}: 4\) weeks \( ightarrow \) can be reduced by 1 week at a cost of \(\$ 1000\)Activity \(\mathrm{Y}: 3\) weeks \( ightarrow \) can be reduced by 2 weeks at \(\$ 800\) per weekActivity Z: 5 weeks \( ightarrow \) can be reduced by 1 week at a cost of \(\$ 1200\)Question:1. Develop a crashing plan to reduce the project timeline to 17 weeks at minimum cost.2. Justify your decision. What considerations should be taken into account when crashing a project?3. How would you monitor the success of the crashing effort during project execution?