Case $1(50$ p$.)$ A project management problem is detailed in the table below. Times are given in weeks. Round all your answers to $4$ digits after the decimal point.

a$.$ p$.)$ Draw the network diagram.

b$.$ p$.)$ Calculate the expected time for each activity.

c$.(10$ p$.)$ Calculate the slack time for each activity.

d$.(10$ p$.)$ Which activities form the critical path? Why are these activities critical?

e$.(5$ p$.)$ What is the estimated time of the critical path?

f$.(5$ p$.)$ What is the project variance?

g$..$