Question 2 - A-Level Maths

Exam Board	OCR
Module	D2 (Decision Mathematics 2)
Year	2009
Session	June
Topic	Curve Sketching
Type	Optimization and assignment problems

Set up a dynamic programming tabulation to find the maximum weight route from ( \(0 ; 0\) ) to ( \(3 ; 0\) ) on the following directed network.
\includegraphics[max width=\textwidth, alt={}, center]{9057da95-c53a-416c-8340-c94aff366385-3_595_1056_404_587} Give the route and its total weight.
The actions now represent the activities in a project and the weights represent their durations. This information is shown in the table below.
Activity Duration Immediate predecessors
\(A\) 8 -
\(B\) 9 -
C 7 -
D 5 \(A\)
E 6 \(A\)
\(F\) 4 \(B\)
\(G\) 5 B
\(H\) 6 \(B\)
\(I\) 10 C
\(J\) 9 \(C\)
\(K\) 6 \(C\)
\(L\) 7 D, F, I
\(M\) 6 \(E , G , J\)
\(N\) 8 \(H\), \(K\)
Make a large copy of the network with the activities \(A\) to \(N\) labelled appropriately. Carry out a forward pass to find the early event times and a backward pass to find the late event times. Find the minimum completion time for the project and list the critical activities.
Compare the solutions to parts (i) and (ii).