PROBLEM $1$

The $\backslash ($ A B C $\backslash )$ Manufacturing Company is considering the construction of a new factory building. The following list shows the project activities, precedence relations and time estimates.

a$)$ Develop a CPM network for the project using the EON$/$AOE approach.

b$)$ Identify the critical path.

c$)$ Compute the total and free floats for the activities.

$\backslash$begin$\{$tabular$\}\{|$c$|$l$|$c$|$c$|\}$

$\backslash$hline Activity & $\backslash$multicolumn$\{1\}\{|$c$|\}\{$ Description $\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Immediate $\backslash \backslash$

Predeoessor$($s$)$

$\backslash$end$\{$tabular$\}$ & Time $\backslash \backslash$

$\backslash$hline A & Problem definition & $-$ & $3\backslash \backslash$

$\backslash$hline B & Preliminary study of costs and constraints & A & $3\backslash \backslash$

$\backslash$hline C & Analysis of problems in existing building & A & $3\backslash \backslash$

$\backslash$hline D & Incorporation of requirements in new building & C & $5\backslash \backslash$

$\backslash$hline E & Detailed drawings of new building & B$,$ C & $6\backslash \backslash$

$\backslash$hline F & Contractor building a prototype & D$,$ E & $9\backslash \backslash$

$\backslash$hline G & Cost analysis & E & $5\backslash \backslash$

$\backslash$hline H & Engineers reviewing feasibility & G & $3\backslash \backslash$

$\backslash$hline I & Contractor building the factory & G$,$ F & $5\backslash \backslash$

$\backslash$hline J & Building inspection & I, H & $6\backslash \backslash$

$\backslash$hline K & Final plant layout & J & $4\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$ PROBLEM $2$

Draw a PERT network diagram for a construction project with the activity information given below.

a$)$ Identify the critical path.

b$)$ Determine the probability of completing the project in two years $(104$ weeks$).$