Consider the following table. All duration estimates are in weeks, and the network proceeds from Node $1$ to Node $8.$ a$.$ Draw an AOA network diagram representing the project. Put the node numbers in circles and draw arrows from node to node, labeling each arrow with the activity letter and estimated time. $($Note: You can either draw on a piece of paper and take a picture and attach the picture or draw using any software and attach the image. $)$

b$.$ Identify and write all of the paths on the network diagram and calculate the length of all the paths.

c$.$ What is the critical path for this project and how long is it$?$

Activity Initial nodes Final Node Estimated duration A $1212$ B $1314$ C $1410$ D $236$ E $2510$ F $344$ G $452$ H $462$ I $564$ J $582$ K $6712$