Question

For a project the following datais given

$\begin{array}{cccc}\text{Activity}& \text{Duration}& \text{Earliest}& \text{Latest}\\ & \text{(in days)}& \text{Start}& \text{Finish}\\ & & \text{Time}& \text{Time}\\ A& 2& 0& 11\\ B& 7& 0& 7\\ C& 8& 0& 11\\ D& 3& 2& 14\\ E& 6& 7& 14\\ F& 10& 7& 17\\ G& 4& 7& 16\\ H& 6& 8& 17\\ I& 2& 13& 16\\ K& 6& 15& 22\end{array}$

The critical path is

• A. $\text{B-E-I-K}$
• B. $\text{A-D-I-J}$
• C. $\text{C-H-J}$
• D. $\text{B-F-J}$

Answer 1

The correct option is D $\text{B-F-J}$

$\begin{array}{ccccccc}\text{Activity}& \text{Duration}& \text{Earliest}& \text{Latest}& \text{Latest}& \text{Total}& \\ & \text{in days}& \text{Start Time}& \text{Finish Time}& \text{Start Time}& \text{Finish Time}& \text{Float}\\ A& 2& 0& 0+2=2& 11-2=9& 11& 9\\ B& 7& 0& 0+7=7& 7-7=0& 7& 0\\ C& 8& 0& 0+8=8& 11-8=3& 11& 3\\ D& 3& 2& 2+3=5& 14-3=11& 14& 9\\ E& 6& 7& 7+6=13& 14-6=8& 14& 1\\ F& 10& 7& 7+10=17& 17-10=7& 0& \\ G& 4& 7& 7+4=11& 16-4=12& 16& 5\\ H& 6& 8& 8+6=14& 17-6=11& 17& 3\\ I& 2& 13& 13+2=15& 16-2=14& 16& 1\\ J& 5& 17& 17+5=22& 22-5=17& 22& 0\\ K& 6& 15& 15+6=21& 22-6=16& 22& 1\end{array}$

$\text{Earliest finish time = Earliest start time + duration}$

$\text{Latest start time = Latest Finish time - Duration}$

$\text{Total float = Latest finish time - Earlist finish time}$

$\text{= Latest start time - Earliest start time}$

For whichever activity total float is zero that activity is on the critical path from the table we observed that total float is zero for B, F, J.

$\text{Hence, the critical path is B-F-J.}$