Questions — Edexcel (9685 questions)

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Edexcel D1 2023 June Q2
6 marks Easy -1.8
2. A list of eleven numbers is to be sorted into descending order. After one pass, the quick sort algorithm produces the following list $$\begin{array} { l l l l l l l l l l l } 17 & 33 & 14 & 25 & 23 & 28 & 21 & 13 & 9 & 6 & 10 \end{array}$$
  1. State, with a reason, which number was used as a pivot for the first pass.
  2. Starting at the left-hand end of the above list, obtain the fully sorted list using a bubble sort. You need to write down only the list that results at the end of each pass.
  3. Apply the first-fit decreasing bin packing algorithm to the fully sorted list to pack the numbers into bins of size 85
Edexcel D1 2023 June Q3
6 marks Easy -1.8
3. In this question, the function \(\operatorname { INT } ( X )\) is the largest integer less than or equal to \(X\). For example, $$\begin{aligned} \mathrm { INT } ( 5.7 ) & = 5 \\ \mathrm { INT } ( 8 ) & = 8 \\ \mathrm { INT } ( - 2.3 ) & = - 3 \end{aligned}$$ Consider the following algorithm.
Step 1 Input \(N\) Step 2 Calculate \(A = N \div 10\) Step 3 Let \(B = \operatorname { INT } ( A )\) Step 4 Calculate \(C = B \times 10\) Step 5 Calculate \(D = N - C\) Step 6 Output \(D\) Step \(7 \quad\) Replace \(N\) by \(B\) Step 8 If \(N = 0\) then STOP, otherwise go back to Step 2
  1. Complete the table in the answer book, using \(N = 4217\), to show the results obtained at each step of the algorithm.
  2. Explain how the output values of the algorithm relate to the original input \(N\), where \(N\) is any positive integer.
Edexcel D1 2023 June Q4
11 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{89702b66-cefb-484b-9c04-dd2be4fe2250-05_1524_1360_203_356} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows the constraints of a linear programming problem in \(x\) and \(y\), where \(R\) is the feasible region. The equations of two of the lines are shown on the graph.
  1. Determine the inequalities that define the feasible region.
  2. Find the exact coordinates of the vertices of the feasible region. The objective is to maximise \(P\), where \(P = 2 x + k y\)
  3. For the case \(k = 3\), use the point testing method to find the optimal vertex of the feasible region and state the corresponding value of \(P\).
  4. Determine the range of values for \(k\) for which the optimal vertex found in (c) is still optimal.
Edexcel D1 2023 June Q5
7 marks Moderate -0.3
5.
ActivityImmediately preceding activities
A-
B-
C-
DA
EA
FB, C, E
GB, C, E
HC
IC
JD, F, G, H, I
KD, F, G, H, I
LI
  1. Draw the activity network described in the precedence table above, using activity on arc and the minimum number of dummies. A project is modelled by the activity network drawn in (a). Each activity requires exactly one worker. The project is to be completed in the shortest possible time. The table below gives the time, in hours, to complete three of the activities.
    ActivityDuration (in hours)
    A10
    E7
    F8
    The length of the critical path AEFK is 33 hours.
  2. Determine the range of possible values for the duration of activity J. You must make your method and working clear.
Edexcel D1 2023 June Q6
13 marks Challenging +1.2
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{89702b66-cefb-484b-9c04-dd2be4fe2250-07_688_1351_203_356} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} [The total weight of the network is 315]
Figure 3 represents a network of roads between nine parks, A, B, C, D, E, F, G, H and J. The number on each edge represents the length, in miles, of the corresponding road.
    1. Use Dijkstra's algorithm to find the shortest path from A to J.
    2. State the length of the shortest path from A to J . The roads between the parks need to be inspected. Robin must travel along each road at least once. Robin wishes to minimise the length of the inspection route. Robin will start the inspection route at C and finish at E .
  2. By considering the pairings of all relevant nodes, find the length of Robin's route.
  3. State the number of times Robin will pass through G . It is now decided to start and finish the inspection route at A. Robin must still minimise the length of the route and travel along each road at least once.
  4. Calculate the difference between the lengths of the two inspection routes.
  5. State the edges that need to be traversed twice in the route that starts and finishes at A , but do not need to be traversed twice in the route that starts at C and finishes at E .
Edexcel D1 2023 June Q7
12 marks Standard +0.3
7.
ABCDEFGH
A-3837\(x\)37424127
B38-263233383734
C3726-3938393039
D\(x\)3239-37362936
E37333837-323330
F4238393632-3128
G413730293331-33
H27343936302833-
The network represented by the table shows the least distances, in km, between eight museums, A, B, C, D, E, F, G and H. A tourist wants to visit each museum at least once, starting and finishing at A. The tourist wishes to minimise the total distance travelled. The shortest distance between A and D is \(x \mathrm {~km}\) where \(32 \leqslant x \leqslant 35\)
  1. Using Prim's algorithm, starting at A , obtain a minimum spanning tree for the network. You must clearly state the order in which you select the arcs of your tree.
  2. Use your answer to (a) to determine an initial upper bound for the length of the tourist's route.
  3. Starting at A, use the nearest neighbour algorithm to find another upper bound for the length of the tourist's route. Write down the route that gives this upper bound. The nearest neighbour algorithm starting at E gives a route of $$\mathrm { E } - \mathrm { H } - \mathrm { A } - \mathrm { D } - \mathrm { G } - \mathrm { C } - \mathrm { B } - \mathrm { F } - \mathrm { E }$$
  4. State which of these two nearest neighbour routes gives the better upper bound. Give reasons for your answer. Starting by deleting A, and all of its arcs, a lower bound of 235 km for the length of the route is found.
  5. Determine the smallest interval that must contain the optimal length of the tourist's route. You must make your method and working clear.
Edexcel D1 2023 June Q8
10 marks Challenging +1.2
8. A headteacher is deciding how to allocate prizes to the students who are leaving at the end of the school year. There are three categories of prize: academic, sport, and leadership.
  • Each academic prize costs \(\pounds 14\), each sport prize costs \(\pounds 8\), and each leadership prize costs \(\pounds 12\). The total amount available to spend on all prizes is \(\pounds 976\)
  • For every 5 academic prizes there must be at least 2 leadership prizes
  • At least half the prizes must be academic
  • \(20 \%\) of the prizes must be for sport
The headteacher wishes to maximise the total number of prizes.
Let \(x , y\) and \(z\) represent the number of academic, sport and leadership prizes respectively.
  1. Formulate this as a linear programming problem in \(x\) and \(y\) only, stating the objective and listing the constraints as simplified inequalities with integer coefficients. Given that the headteacher awards 16 sport prizes,
  2. calculate the corresponding number of leadership prizes that the headteacher awards. You must show your working.
Edexcel D1 2024 June Q1
14 marks Easy -1.2
1.
5.24.76.54.53.15.11.82.93.43.81.2
  1. Use the first-fit bin packing algorithm to determine how the eleven numbers listed above can be packed into bins of size 14
  2. The list of numbers is to be sorted into ascending order. Use a quick sort to obtain the sorted list. You should show the result of each pass and identify your pivots clearly.
  3. Apply the first-fit decreasing bin packing algorithm to the sorted list to pack the numbers into bins of size 14
  4. Explain why the number of bins used in part (c) is optimal.
  5. Use the binary search algorithm to try to locate 3.0 in the list of numbers. Clearly indicate how you choose your pivots and which part of the list is rejected at each stage.
Edexcel D1 2024 June Q2
10 marks Standard +0.3
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba9337bf-7a3c-49aa-b395-dd7818cf1d13-03_942_1587_242_239} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} [The sum of the durations of all the activities is 59 days.]
The network in Figure 1 shows the activities that need to be undertaken to complete a project. Each activity is represented by an arc and the duration, in days, of the corresponding activity is shown in brackets. Each activity requires one worker. The project is to be completed in the shortest possible time.
    1. Complete Diagram 1 in the answer book to show the early event times and the late event times.
    2. State the minimum completion time of the project.
  2. Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
  3. Schedule the activities using the minimum number of workers so that the project is completed in the minimum time.
Edexcel D1 2024 June Q3
8 marks Easy -1.2
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba9337bf-7a3c-49aa-b395-dd7818cf1d13-04_994_1616_242_223} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 models a network of tracks between nine ranger stations, A, B, C, D, E, F, G, H and J, in a forest. The number on each edge gives the time, in minutes, to travel along the corresponding track. The forest ranger wishes to travel from A to J as quickly as possible.
  1. Use Dijkstra's algorithm to find the shortest time needed to travel from A to J. State the quickest route.
    (6)
  2. Hence determine the weight of the minimum spanning tree for the network given in Figure 2. Give a reason for your answer. You do not need to find the minimum spanning tree.
Edexcel D1 2024 June Q4
14 marks Moderate -0.5
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba9337bf-7a3c-49aa-b395-dd7818cf1d13-06_873_1620_242_223} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} [The total weight of the network is 494]
Direct roads between nine factories, A, B, C, D, E, F, G, H and J, are represented in Figure 3. The number on each arc represents the lengths, in kilometres, of the corresponding road.
The table below shows the shortest distances, in kilometres, between the nine factories.
ABCDEFGHJ
A-157251542645146
B15-22403057493631
C722-322249715853
D254032-1017577071
E15302210-27676661
F4257491727-405372
G644971576740-1332
H51365870665313-19
J4631537161723219-
\section*{Table of shortest distances}
  1. Starting at A, use Prim's algorithm to find a minimum spanning tree for the table of shortest distances. You must state the order in which you select the arcs of your tree.
    (3)
  2. State the weight of the minimum spanning tree.
    (1) A route is needed that minimises the total distance to traverse each road at least once. The route must start at E and finish at F .
  3. Determine the length of this route. You must give a reason for your answer. It is now decided to start the route at C and finish the route at A . The route must include every road at least once and must still minimise the total distance travelled.
  4. By considering the pairings of all relevant nodes, find the roads that need to be traversed twice. Naoko needs to visit all nine factories, starting and finishing at the same factory, and wishes to minimise the total distance travelled.
  5. Starting at B, use the nearest neighbour algorithm on the table of shortest distances to find an upper bound for the length of Naoko's route. Write down the cycle, obtained from the table of shortest distances, which gives this upper bound.
  6. By deleting C and all of its arcs, use the values in the table of shortest distances to find a lower bound for the length of Naoko's route.
Edexcel D1 2024 June Q5
10 marks Standard +0.8
5. The head of a Mathematics department needs to order three types of paper. The three types of paper are plain, lined and graph. All three types of paper are sold in reams. (A ream is 500 sheets of paper.)
Based on the last academic year the head of department formed the following constraints.
  • At least half the paper must be lined
  • No more than \(15 \%\) of the paper must be graph paper
  • The ratio of plain paper to graph paper must be \(5 : 2\)
The cost of each ream of plain, lined and graph paper is \(\pounds 5 , \pounds 12\) and \(\pounds 15\) respectively. The head of department has at most \(\pounds 834\) to spend on paper. The head of department wants to maximise the total number of reams of paper ordered.
Let \(x , y\) and \(z\) represent the number of reams of plain paper, lined paper and graph paper ordered respectively.
  1. Formulate this information as a linear programming problem in \(x\) and \(y\) only, stating the objective and listing the constraints as simplified inequalities with integer coefficients. The head of department decides to order exactly 42 reams of lined paper and still wishes to maximise the total number of reams of paper ordered.
  2. Determine
    1. the total number of reams of paper to be ordered,
    2. the number of reams of graph paper to be ordered.
Edexcel D1 2024 June Q6
10 marks Moderate -0.3
6.
ActivityImmediately preceding activities
A-
B-
CA
D-
EA, B, D
FD
GA, B, D
HF, G
IA
JF, G
KC, E, H, I
LI
MC, E, H, I
  1. Draw the activity network for the project described in the precedence table, using activity on arc and the minimum number of dummies. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{ba9337bf-7a3c-49aa-b395-dd7818cf1d13-10_880_1154_1464_452} \captionsetup{labelformat=empty} \caption{Grid 1}
    \end{figure} A cascade chart for all the activities of the project, except activity \(\mathbf { L }\), is shown on Grid 1. The time taken to complete each activity is given in hours and each activity requires one worker. The project is to be completed in the minimum time using as few workers as possible.
  2. State the critical activities of the project.
  3. Use the cascade chart to determine the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities. (You do not need to provide a schedule of the activities.) The duration of activity L is \(x\) hours. Given that the total float of activity L is at most 7 hours,
  4. determine the range of possible values for \(\chi\).
Edexcel D1 2021 October Q1
10 marks Moderate -0.8
  1. (a) Explain what is meant by the term 'path'.
    (2)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-02_812_1262_427_404} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 represents a network of roads. The number on each arc represents the length, in km, of the corresponding road. Piatrice wishes to travel from A to J.
(b) Use Dijkstra's algorithm to find the shortest path Piatrice could take from A to J. State your path and its length.
(6) Piatrice needs to return from J to A via G.
(c) Find the shortest path Piatrice could take from J to A via G and state its length.
Edexcel D1 2021 October Q2
6 marks Moderate -0.3
2. Chris has been asked to design a badge in the shape of a triangle XYZ subject to the following constraints.
  • Angle \(Y\) should be at least three times the size of angle \(X\)
  • Angle \(Z\) should be at least \(50 ^ { \circ }\) larger than angle \(X\)
  • Angle \(Y\) must be at most \(120 ^ { \circ }\)
Chris has been asked to maximise the sum of the angles \(X\) and \(Y\).
Let \(x\) be the size of angle \(X\) in degrees.
Let \(y\) be the size of angle \(Y\) in degrees.
Let z be the size of angle \(Z\) in degrees.
Formulate this information as a linear programming problem in \(x\) and \(y\) only. State the objective and list the constraints as simplified inequalities with integer coefficients. You are not required to solve this problem.
Edexcel D1 2021 October Q3
15 marks Moderate -0.3
3. The table below represents a complete network that shows the least costs of travelling between eight cities, A, B, C, D, E, F, G and H.
ABCDEFGH
A-36384023393835
B36-353635344138
C3835-3925324040
D403639-37372633
E23352537-422443
F3934323742-4538
G384140262445-40
H35384033433840-
Srinjoy must visit each city at least once. He will start and finish at A and wishes to minimise his total cost.
  1. Use Prim's algorithm, starting at A , to find a minimum spanning tree for this network. You must list the arcs that form the tree in the order in which you select them.
  2. State the weight of the minimum spanning tree.
  3. Use your answer to (b) to help you calculate an initial upper bound for the total cost of Srinjoy’s route.
  4. Show that there are two nearest neighbour routes that start from A. You must make the routes and their corresponding costs clear.
  5. State the best upper bound that can be obtained by using your answers to (c) and (d).
  6. Starting by deleting A and all of its arcs, find a lower bound for the total cost of Srinjoy’s route. You must make your method and working clear.
  7. Use your results to write down the smallest interval that must contain the optimal cost of Srinjoy's route.
Edexcel D1 2021 October Q4
11 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-06_757_1163_226_459} \captionsetup{labelformat=empty} \caption{Figure 2}
\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.
  1. 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}
  2. 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.
  3. Calculate a lower bound for the minimum number of workers required. You must show your working.
  4. 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.
  5. State the new minimum project completion time and state the new critical path.
Edexcel D1 2021 October Q5
10 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-08_588_1428_230_322} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} [The total weight of the network is 166] Figure 3 models a network of cycle lanes that must be inspected. The number on each arc represents the length, in km, of the corresponding cycle lane. Lance needs to cycle along each lane at least once and wishes to minimise the length of his inspection route. He must start and finish at A.
  1. Use an appropriate algorithm to find the length of the route. State the cycle lanes that Lance will need to traverse twice. You should make your method and working clear.
    (6)
  2. State the number of times that vertex C appears in Lance's route.
    (1) It is now decided that the inspection route may finish at any vertex. Lance will still start at A and must cycle along each lane at least once.
  3. Determine the finishing point so that the length of the route is minimised. You must give reasons for your answer and state the length of this new minimum route.
    (3)
Edexcel D1 2021 October Q6
13 marks Standard +0.3
6. A linear programming problem in \(x\) and \(y\) is described as follows. Maximise \(P = k x + y\), where \(k\) is a constant
subject to: \(\quad 3 y \geqslant x\) $$\begin{aligned} x + 2 y & \leqslant 130 \\ 4 x + y & \geqslant 100 \\ 4 x + 3 y & \leqslant 300 \end{aligned}$$
  1. Add lines and shading to Diagram 1 in the answer book to represent these constraints. Hence determine the feasible region and label it \(R\).
  2. For the case when \(k = 0.8\)
    1. use the objective line method to find the optimal vertex, \(V\), of the feasible region. You must draw and label your objective line and label vertex \(V\) clearly.
    2. calculate the coordinates of \(V\) and hence calculate the corresponding value of \(P\) at \(V\). Given that for a different value of \(k , V\) is not the optimal vertex of \(R\),
  3. determine the range of possible values for \(k\). You must make your method and working clear.
Edexcel D1 2021 October Q7
10 marks Moderate -0.8
7. The numbers listed below are to be packed into bins of size \(n\), where \(n\) is a positive integer.
14
20
23
17
15
22
19
25
Edexcel D1 2021 October Q20
Easy -1.2
20
23
17
15
22
19
25
13
28
32 A lower bound for the number of bins required is 4
  1. Determine the range of possible values of \(n\). You must make your method clear.
    (3)
  2. Carry out a quick sort to produce a list of the numbers in descending order. You should show the result of each pass and identify your pivots clearly.
    (4) When the first-fit bin packing algorithm is applied to the original list of numbers, the following allocation is achieved. \end{table}
    \includegraphics[max width=\textwidth, alt={}]{d409aaae-811d-4eca-b118-efc927885f97-14_1193_1586_1270_185}
    Shortest path from A to J: \(\_\_\_\_\) Length of shortest path from A to J: \(\_\_\_\_\) \section*{2. \(\_\_\_\_\)} \section*{3.}
    ABCDEFGH
    A-36384023393835
    B36-353635344138
    C3835-3925324040
    D403639-37372633
    E23352537-422443
    F3934323742-4538
    G384140262445-40
    H35384033433840-
    ABCDEFGH
    A-36384023393835
    B36-353635344138
    C3835-3925324040
    D403639-37372633
    E23352537-422443
    F3934323742-4538
    G384140262445-40
    H35384033433840-
    ABCDEFGH
    A-36384023393835
    B36-353635344138
    C3835-3925324040
    D403639-37372633
    E23352537-422443
    F3934323742-4538
    G384140262445-40
    H35384033433840-
    ABCDEFGH
    A-36384023393835
    B36-353635344138
    C3835-3925324040
    D403639-37372633
    E23352537-422443
    F3934323742-4538
    G384140262445-40
    H35384033433840-
    4. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-22_755_1157_246_404} \captionsetup{labelformat=empty} \caption{Figure 2}
    \end{figure}
  3. Activity
    Immediately
    preceding
    activities
    A
    B
    C
    D
    E
    Activity
    Immediately
    preceding
    activities
    F
    G
    H
    I
    J
    Activity
    Immediately
    preceding
    activities
    K
    L
    M
    $$v = \ldots \quad x = \ldots \quad y = \ldots$$ \includegraphics[max width=\textwidth, alt={}, center]{d409aaae-811d-4eca-b118-efc927885f97-23_2255_56_315_37}
    \includegraphics[max width=\textwidth, alt={}]{d409aaae-811d-4eca-b118-efc927885f97-23_1153_1338_303_310}
    \section*{Grid 2} 5. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{d409aaae-811d-4eca-b118-efc927885f97-24_591_1433_255_260} \captionsetup{labelformat=empty} \caption{Figure 3
    [0pt] [The total weight of the network is 166]}
    \end{figure} 6.
    \includegraphics[max width=\textwidth, alt={}]{d409aaae-811d-4eca-b118-efc927885f97-26_1287_1645_301_162}
    \section*{Diagram 1} 7. \(\begin{array} { l l l l l l l l l l l } 14 & 20 & 23 & 17 & 15 & 22 & 19 & 25 & 13 & 28 & 32 \end{array}\)
Edexcel D1 2013 Specimen Q1
8 marks Easy -1.8
1.
Hajra
\(( \mathrm { H } )\)
Vicky
\(( \mathrm { V } )\)
Leisham
\(( \mathrm { L } )\)
Alice
\(( \mathrm { A } )\)
Nicky
\(( \mathrm { N } )\)
June
\(( \mathrm { J } )\)
Sharon
\(( \mathrm { S } )\)
Tom
\(( \mathrm { T } )\)
Paul
\(( \mathrm { P } )\)
The table shows the names of nine people.
  1. Use a quick sort to produce the list of names in ascending alphabetical order. You must make your pivots clear.
  2. Use the binary search algorithm on your list to locate the name Paul.
Edexcel D1 2013 Specimen Q2
9 marks Easy -1.2
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5fa867a2-0a3d-4f0b-9f9c-15584f2be5c0-03_719_1161_223_452} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 represents the distances, in metres, between eight vertices, \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F } , \mathrm { G }\) and H , in a network.
  1. Use Kruskal's algorithm to find a minimum spanning tree for the network. You should list the arcs in the order in which you consider them. In each case, state whether you are adding the arc to your minimum spanning tree.
  2. Complete Matrix 1 in your answer book, to represent the network.
  3. Starting at A, use Prim's algorithm to determine a minimum spanning tree. You must clearly state the order in which you considered the vertices and the order in which you included the arcs.
  4. State the weight of the minimum spanning tree.
Edexcel D1 2013 Specimen Q3
9 marks Easy -1.8
3. $$\begin{array} { l l l l l l l } 41 & 28 & 42 & 31 & 36 & 32 & 29 \end{array}$$ The numbers in the list represent the weights, in kilograms, of seven statues. They are to be transported in crates that will each hold a maximum weight of 60 kilograms.
  1. Calculate a lower bound for the number of crates that will be needed to transport the statues.
  2. Use the first-fit bin packing algorithm to allocate the statues to the crates.
  3. Use the full bin algorithm to allocate the statues to the crates.
  4. Explain why it is not possible to transport the statues using fewer crates than the number needed for part (c).
Edexcel D1 2013 Specimen Q4
10 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5fa867a2-0a3d-4f0b-9f9c-15584f2be5c0-05_879_1068_248_497} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} [The total weight of the network is 73.3 km ]
Figure 2 models a network of tunnels that have to be inspected. The number on each arc represents the length, in km , of that tunnel.
Malcolm needs to travel through each tunnel at least once and wishes to minimise the length of his inspection route.
He must start and finish at A .
  1. Use the route inspection algorithm to find the tunnels that will need to be traversed twice. You should make your method and working clear.
  2. Find a route of minimum length, starting and finishing at A . State the length of your route. A new tunnel, CG, is under construction. It will be 10 km long.
    Malcolm will have to include the new tunnel in his inspection route.
  3. What effect will the new tunnel have on the total length of his route? Justify your answer.