create the Network diagram and PERT chart for the project. The tasks and the predecessors have been identified and listed in the following table.

$\backslash$table$[[$Task$,$Task Name,$\backslash$table$[[$Duration$],[($In days$)]],$Predecessors$],[$A$,\backslash$table$[[$Preliminary investigation$],[$and planning$]],5,-],[$B$,$User requirement analysis,$4,$A$],[$C$,$Process modeling,$12,$B$],[$D$,$Data modeling,$6,$B$],[$E$,$Program design,$18,$C$,$ D$],[$F$,$Database design,$8,$D$],[$G$,$Interface design,$9,$B$],[$H$,\backslash$table$[[$Programming and unit$],[$testing$]],20,$E$,$ F$],[$I$,$System testing,$6,$G$,$ H$],[$J$,$Installation,$8,$I$]]$

Draw a network diagram, then expand it into a PERT Chart in MS Visio. Note: please complete the following questions to get full credits as each question has assigned points $($refer to the grading rubric on Canvas$).$

a$.$ Based on the network diagram you created, list all paths in your network diagram and calculate the length of each path. Then, mark the critical path.

b$.$ Create the PERT chart $($Remember to calculate the Early Start $($ES$),$ Early Finish $($EF$),$ Late Start $($LS$),$ Late Finish $($LF$),$ as well as the Total Slack and Free Slack for each activity.

c$.$ Highlight the critical path in your PERT chart and write down in a textbox: the duration of the project $($how many days$).$