4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-06_757_1163_226_459}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

The network in Figure 2 shows the activities that need to be carried out by a company to complete a project. Each activity is represented by an arc, and the duration, in days, is shown in brackets. Each activity requires one worker. The early event times and the late event times are shown at each vertex.
\begin{enumerate}[label=(\alph*)]
\item Complete the precedence table in the answer book.\\
(2)

A cascade chart for this project is shown on Grid 1.\\
\includegraphics[max width=\textwidth, alt={}, center]{d409aaae-811d-4eca-b118-efc927885f97-07_885_1358_276_356}

\section*{Grid 1}
\item Use Figure 2 and Grid 1 to find the values of $v , w , x , y$ and $z$.

The project is to be completed in the minimum time using as few workers as possible.
\item Calculate a lower bound for the minimum number of workers required. You must show your working.
\item On Grid 2 in your answer book, construct a scheduling diagram for this project.

Before the project begins it is found that activity F will require an additional 5 hours to complete. The durations of all other activities are unchanged. The project is still to be completed in the shortest possible time using as few workers as possible.
\item State the new minimum project completion time and state the new critical path.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D1 2021 Q4 [11]}}