Part $1$: Planning and Execution Before Challenges Tasks List Task Task Description Duration Dependencies Resources ID T$1$ Initial meetings for requirements $2$ weeks NoneAlex, Maya Marketing T$2$ Market analysis and feasibility study $3$ weeks None Team T$3$ Drafting initial project plan $1$ week T$1$ Alex Setting up development T$41$ week None Tech Support environment Jamie T$5$ Algorithm development $3$ weeks T$3$T$4$ Developers Sam, Design T$6/$UX design $4$ weeks T$3$ Team T$7$ integration$2$ weeks T$5$Backend Team Initial testing T$81$ week T$5$T$6$QA Team $($ Algorithm $)$ T$9$ Feedback incorporation $2$ weeks T$8$All Teams. Question Part $2$A: Identify the Initial Critical Path Based on the task list and durations provided in Part $1$: Identify the Critical Path: Determine the sequence of tasks that directly impacts the project's total duration. Explain your rationale for each task's inclusion on the critical path $.$ Calculate the Project Duration : Sum the durations of the tasks on the critical path to estimate the minimum project completion time. Adjusted Task Durations : To simulate the dynamic nature of project management $,$ assume the following changes in task durations due to unforeseen circumstances : T$4$: Duration increases to $4$ weeks $.$ T$5$: Algorithm development duration increase to $6$ weeks due to a technological challenge $.$ : UI $/$UX design duration increases to $5$ weeks due to additional user testing requirements Question Part $2$B : Re $-$Identify the Critical Path with Adjusted Durations Given the changes in task durations : Re$-$Identify the Critical Path : Determine how the adjustments in task durations affect the critical path $.$ Indicate any changes in the sequence of critical tasks Recalculate the Project Duration : Provide a new estimate for the minimum