MST with cost calculation

A question is this type if and only if it asks you to calculate actual monetary cost based on MST length and a given cost per unit length.

2 questions · Moderate -0.7

7.04b Minimum spanning tree: Prim's and Kruskal's algorithms
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AQA Further AS Paper 2 Discrete 2018 June Q6
5 marks Moderate -0.8
6 An animal sanctuary has a rainwater collection site. The manager of the sanctuary is installing a pipe system to connect the rainwater collection site to five other sites in the sanctuary. Each site does not need to be connected directly to the rainwater collection site. There are nine possible routes between the sites that are suitable for water pipes. The distances, in metres, of the nine possible routes are given in the table below.
From/ToHenhouse (H)Goatshed (G)Kennels (K)Cattery (C)
Rainwater collection site (R)840810520370
Cattery (C)-680610\multirow{3}{*}{}
Duckpond (D)480310
Goatshed (G)150
Water pipe costs 60 pence per metre. Find the minimum cost of connecting all the sites to the rainwater collection site. Fully justify your answer. \(7 \quad\) A linear programming problem has the constraints $$\begin{aligned} 1 \leq x & \leq 6 \\ 1 \leq y & \leq 6 \\ y & \geq x \\ x + y & \leq 11 \end{aligned}$$
AQA Further Paper 3 Discrete 2020 June Q3
8 marks Moderate -0.5
3 A company is installing an internal telephone network between the offices in a council building. Each office is required to be connected with telephone cables, either directly or indirectly, to every other office in the building. The lengths of cable, in metres, needed to connect the offices are shown in the table below.
EducationHousingRefuse CollectionPayrollSocial CareTransport
Education-2713351624
Housing27-29302224
Refuse Collection1329-262317
Payroll353026-2040
Social Care16222320-21
Transport2424174021-
The council wants the total length of cable that is used to be as small as possible.
The cost to the council to install one metre of cable is \(\pounds 8\) 3
    1. Find the minimum total cost to the council to install the cable required for the internal telephone network.
      [0pt] [4 marks]
      3
      1. (ii) Suggest a reason why the total cost to the council for installing the internal telephone network is likely to be different from your answer to part (a)(i). 3
    2. Before the company starts installing the cable, it is told that the Education office cannot be connected directly to the Transport office due to issues with the building. Explain the possible impact of this on your answer to part (a)(i).