Space Module Assembly. An aerospace company has received a contract from NASA for the final assembly of a space module for an upcoming mission. A team of engineers has determined the activities, precedence constraints, and time estimates as given in Table $9\mathrm{.}19.$

TABLE $9\mathrm{.}19$

ActivitySymbolImmediate predecessorsTime estimate $($days$)$Construct shell of moduleA$30$Order life support system and scientific experimentation package from same supplierB$15$Order components of control and navigational systemC$25$Wire moduleDA$3$Assemble control and navigational systemEC$7$Preliminary test of life support systemFB$1$Install life support in moduleGD, F$5$Install scientific experimentation package in moduleHD, F$2$Preliminary test of control and navigational systemIE, F$4$Install control and navigational system in moduleJH, I$10$Final testing and debuggingKG, J$8$

a$.$Draw the AOA network for this project. $($Hint: You should have $10$ events and two dummy activities.$)$

b$.$Calculate total slacks and free slacks, and interpret their meaning.

c$.$Determine the critical path and interpret its meaning.

d$.$Construct a Gantt chart and identify scheduling flexibilities.