Edexcel FD1 AS (Further Decision 1 AS) 2020 June

1. \(3.7 \quad 2.5\)
\(5.4 \quad 1.9\)
2.7
3.2
3.1
2.7
4.2
2.0

1. Use the first-fit bin packing algorithm to determine how the numbers listed above can be packed into bins of size 8.5 The first-fit bin packing algorithm is to be used to pack \(n\) numbers into bins. The number of comparisons is used to measure the order of the first-fit bin packing algorithm.
2. By considering the worst case, determine the order of the first-fit bin packing algorithm in terms of \(n\). You must make your method and working clear.

2. \begin{figure}[h] \end{figure} A project is modelled by the activity network shown in Figure 1. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity. Each activity requires one worker. The project is to be completed in the shortest possible time.

1. Complete the precedence table in the answer book.
2. Complete Diagram 1 in the answer book to show the early event times and the late event times.
3. 1. State the minimum project completion time.
   2. List the critical activities.
4. Calculate the maximum number of hours by which activity H could be delayed without affecting the shortest possible completion time of the project. You must make the numbers used in your calculation clear.
5. Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
6. Draw a cascade chart for this project on Grid 1 in the answer book.
7. Using the answer to (f), explain why it is not possible to complete the project in the shortest possible time using the number of workers found in (e).

3. \begin{figure}[h] \end{figure} [The weight of the network is \(5 x + 246\) ]

1. Explain why it is not possible to draw a graph with an odd number of vertices of odd valency. Figure 2 represents a network of 14 roads in a town. The expression on each arc gives the time, in minutes, to travel along the corresponding road. Prim's algorithm, starting at A, is applied to the network. The order in which the arcs are selected is \(\mathrm { AD } , \mathrm { DH } , \mathrm { DG } , \mathrm { FG } , \mathrm { EF } , \mathrm { CG } , \mathrm { BD }\). It is given that the order in which the arcs are selected is unique.
2. Using this information, find the smallest possible range of values for \(x\), showing your working clearly. A route that minimises the total time taken to traverse each road at least once is required. The route must start and finish at the same vertex. Given that the time taken to traverse this route is 318 minutes,
3. use an appropriate algorithm to determine the value of \(x\), showing your working clearly.

4. \begin{figure}[h] \end{figure} Figure 3 shows the constraints of a linear programming problem in \(x\) and \(y\), where \(R\) is the feasible region. Figure 3 also shows an objective line for the problem and the optimal vertex, which is labelled as \(V\). The value of the objective at \(V\) is 556
Express the linear programming problem in algebraic form. List the constraints as simplified inequalities with integer coefficients and determine the objective. Please check the examination details below before entering your candidate information
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□ \section*{Thursday 14 May 2020} Afternoon
Paper Reference 8FMO/27 \section*{Further Mathematics} Advanced Subsidiary
Further Mathematics options
27: Decision Mathematics 1
(Part of options D, F, H and K) \section*{Answer Book} Do not return the question paper with the answer book.
1.
\(\begin{array} { l l l l l l l l l l } 3.7 & 2.5 & 5.4 & 1.9 & 2.7 & 3.2 & 3.1 & 2.7 & 4.2 & 2.0 \end{array}\)

1. (a)

\begin{figure}[h] \end{figure} \begin{figure}[h] \end{figure} 3. \begin{figure}[h] \end{figure} [The weight of the network is \(5 x + 246\) ] 4. \begin{figure}[h] \end{figure}