Edexcel FD1 AS (Further Decision 1 AS) 2022 June

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The list of eleven numbers shown above is to be sorted into ascending order.

1. Carry out a quick sort to produce the sorted list. You should show the result of each pass and identify your pivots clearly.
   (4) \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{c8134d3b-71cb-4b92-ac54-81a4ff8f3011-03_814_1545_614_260} \captionsetup{labelformat=empty} \caption{Figure 1}
   \end{figure}
2. Use Kruskal's algorithm to find the minimum spanning tree for the network in Figure 1. You should list the arcs in the order in which you consider them. For each arc, state whether or not you are adding it to your minimum spanning tree.
3. 1. Draw the minimum spanning tree on Diagram 1 in the answer book.
   2. State the total weight of the tree.

2.

1. Draw the activity network described in the precedence table above, using activity on arc. Your activity network must contain the minimum number of dummies only.
2. Explain why it is necessary to draw a dummy from the end of activity A . Every activity shown in the precedence table has the same duration.
3. State which activity cannot be critical, justifying your answer.

3. \begin{figure}[h] \end{figure} [The total weight of the network is 120]

1. Explain what is meant by the term "path".
2. State, with a reason, whether the network in Figure 2 is Eulerian, semi-Eulerian or neither. Figure 2 represents a network of cycle tracks between eight villages, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F } , \mathrm { G }\) and H . The number on each arc represents the length, in km , of the corresponding track. Samira lives in village A, and wishes to visit her friend, Daisy, who lives in village H.
3. Use Dijkstra's algorithm to find the shortest path that Samira can take. An extra cycle track of length 9 km is to be added to the network. It will either go directly between C and D or directly between E and G . Daisy plans to cycle along every track in the new network, starting and finishing at H .
   Given that the addition of either track CD or track EG will not affect the final values obtained in (c),
4. use a suitable algorithm to find out which of the two possible extra tracks will give Daisy the shortest route, making your method and working clear. You must
   • state which tracks Daisy will repeat in her route
   • state the total length of her route

4. \begin{figure}[h] \end{figure} Figure 3 shows the constraints of a maximisation linear programming problem in \(x\) and \(y\), where \(x \geqslant 0\) and \(y \geqslant 0\). The unshaded area, including its boundaries, forms the feasible region, \(R\). An objective line has been drawn and labelled on the graph.

1. List the constraints as simplified inequalities with integer coefficients. The optimal value of the objective function is 216
2. 1. Calculate the exact coordinates of the optimal vertex.
   2. Hence derive the objective function. Given that \(x\) represents the number of small flower pots and \(y\) represents the number of large flower pots supplied to a customer,
3. deduce the optimal solution to the problem. TOTAL FOR DECISION MATHEMATICS 1 IS 40 MARKS END