Topic: Project Management (PERT and CPM) Instruction: Solve the following problem using PERT or CPM. 1. The Sofia Academy is considering building a new athletic complex on campus. The complex would provide a new gymnasium for inter-school sports activities, expanded office space, classrooms, and intramural facilities. The following activities would have to be undertaken before construction starts. a. Construct the project network b. Determine the critical path c. Find the completion time of the project d. Make a Gantt chart of the activities 2. A promoter of championship boxing match must perform the task shown in the table before the boxing match can be held (all durations in days). a. Construct tne project network b. Determine the critical path c. Find the completion time of the project d. Make a Gantt chart of the activities 3. Consider the list of activities and predecessors that are involved in constructing a house in the table below. a. Draw a network diagram and determine the expected project completion time b. What is the probability that the project completion time will meet the 35-day deadline? c. Make the gantt chart of the project. 4. Consider the project a. Construct the rtKI network diagram tor this project. b. Compute the mean and variance in time for each activity c. Find the critical path and determine the expected length of the critical path? d. Assuming normality and path independence, what is the probability of meeting the 72 -week deadline