7. This question should be answered on the sheet provided. \begin{figure}[h] \end{figure} The activity network in Figure 5 models the work involved in laying the foundations and putting in services for an industrial complex. The activities are represented by the arcs and the numbers in brackets give the time, in days, to complete each activity. Activity \(C\) is a dummy.

1. Execute a forward scan to calculate the early times and a backward scan to calculate the late times, for each event.
2. Determine which activities lie on the critical path and list them in order.
3. State the minimum length of time needed to complete the project. The contractor is committed to completing the project in this minimum time and faces a penalty of \(\pounds 50000\) for each day that the project is late. Unfortunately, before any work has begun, flooding means that activity \(F\) will take 3 days longer than the 7 days allocated.
4. Activity \(N\) could be completed in 1 day at an extra cost of \(\pounds 90000\). Explain why doing this is not economical.
   (3 marks)
5. If the time taken to complete any one activity, other than \(F\), could be reduced by 2 days at an extra cost of \(\pounds 80000\), for which activities on their own would this be profitable. Explain your reasoning.
   (3 marks) END \section*{Please hand this sheet in for marking}

   	A	B	C	D	E	\(F\)
   A	-	130	190	155	140	125
   B	130	-	215	200	190	170
   C	190	215	-	110	180	100
   D	155	200	110	-	70	45
   E	140	190	180	70	-	75
   \(F\)	125	170	100	45	75	-

   \section*{Please hand this sheet in for marking}

6. \(n\)	\(x _ { n }\)	\(а\)	Any more data?	\(x _ { n + 1 }\)	\(b\)	\(( b - a ) > 0\) ?	\(a\)
   1	8	8	Yes	2	2	No	2
   2	-	-

   Final output
7. \(\_\_\_\_\)
   Sheet for answering question 3
   NAME \section*{Please hand this sheet in for marking}
9. 1. 
      \includegraphics[max width=\textwidth, alt={}, center]{acc09687-11a3-4392-af17-3d4d331d5ab4-11_716_1218_502_331}
   2. 
      \includegraphics[max width=\textwidth, alt={}, center]{acc09687-11a3-4392-af17-3d4d331d5ab4-11_709_1214_1498_333} Maximum flow =
10. 1. \(\_\_\_\_\)
    2. \(\_\_\_\_\)
       \section*{Please hand this sheet in for marking}
11. 
    \includegraphics[max width=\textwidth, alt={}, center]{acc09687-11a3-4392-af17-3d4d331d5ab4-12_764_1612_402_255}
12. \(\_\_\_\_\)
13. \(\_\_\_\_\)
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15. \(\_\_\_\_\)