For a particular project, six activities are to be carried out. The precedence relation and duration of activities are as per the following table. The minimum project completion time (in days) is 

Activity	Immediate predecessor	Duration (days)
A	--	6
B	A	5
C	A	8
D	B	11
E	C	6
F	D, E	7

Correct option is C

​$$\textbf{Draw the Network Diagram} \\1. \ \text{Start} \rightarrow A \rightarrow B \rightarrow D \rightarrow F \rightarrow \text{End} \\\text{(Path: A-B-D-F, Duration: } 6 + 5 + 11 + 7 = \textbf{29 days)} \\\\2. \ \text{Start} \rightarrow A \rightarrow C \rightarrow E \rightarrow F \rightarrow \text{End} \\\text{(Path: A-C-E-F, Duration: } 6 + 8 + 6 + 7 = \textbf{27 days)} \\\\\textbf{Identify the Critical Path} \\\text{The longest path determines the project duration.} \\\textbf{A-B-D-F (29 days)} \text{ is longer than A-C-E-F (27 days).} \\\text{Thus, the critical path is } \boxed{A \rightarrow B \rightarrow D \rightarrow F}. \\\\\textbf{Calculate Minimum Project Completion Time} \\\text{The project cannot be completed faster than the critical path duration:} \\\text{Minimum Completion Time} = 6\,(\text{A}) + 5\,(\text{B}) + 11\,(\text{D}) + 7\,(\text{F}) = \boxed{29\, \text{days}}$$​​