PROJECT MANAGEMENT. A new software installation project has been defined to contain the following key activities. The duration (months), costs, and predecessor relationships for each project activity are shown in the table helnow a. Draw the Activity-on-Node and the Critical Path Method network diagrams for this project, and identify the expected project completion time. [4 Marks] b. What is the project network's critical path? [ 1 Mark ] c. Find the lowest-cost option for completing ('crashing') the project three months early. Show your calculations in detail. [2 Marks] d. Prove that your lowest-cost option to "crash" the project by three months is actually a valid solution, and identify how the 'original' critical path has been affected. Show your calculations in detail. [4 Marks] e. Calculate the new total project cost after the '3-months' crash. [1 Mark ]