Formulating linear programmes: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 4.1 Formulating linear programmes, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 27 questions on Formulating linear programmes, as a list

June 2025, Modelling with Algorithms, Q1 (6 marks): Four workers, Ali (A), Beth (B), Casey (C) and Dev (D), are available to complete three tasks, P, Q and R. Each worker can only be assigned to at most one task,
June 2025, AS Modelling with Algorithms, Q5 (12 marks): The diagram represents a system of pipes through which water flows continuously from a source S to a sink T. The weights on the arcs show the capacities of the
June 2025, AS Modelling with Algorithms, Q7 (12 marks): The diagram shows an activity network for a project. Each activity is represented by an arc. The expressions in brackets show the duration of these activities i
June 2024, Modelling with Algorithms, Q3 (11 marks): A directed network consists of eight nodes, S, A, B, C, D, E, F and T, and seventeen arcs. The arcs represent a system of pipes through which a fluid flows cont
June 2024, Modelling with Algorithms, Q4 (8 marks): A student is trying to draw a triangle XYZ subject to the following constraints. • Angle X must be at most 10° smaller than angle Z. • Angle Y must be at least
June 2024, Modelling with Algorithms, Q6 (13 marks): A maximisation LP problem in x, y and z is to be solved. The tableau after the 1st iteration of the simplex method is shown below. P x y z s1 s2 s3 RHS 1 0 0 0
June 2024, AS Modelling with Algorithms, Q4 (10 marks): A student sets up the following initial tableau in Fig. 4.1 to solve a maximisation LP problem in x, y, and z. Fig. 4.1 P x y z s1 s2 s3 RHS 1 -2 3 -1 0 0 0 0 0
June 2024, AS Modelling with Algorithms, Q5 (15 marks): The objective function for a LP formulation to find the shortest path from A to G in a network with seven vertices, A, B,…, G is given below. Minimise 5AB + 13A
June 2024, AS Modelling with Algorithms, Q6 (12 marks): Each year, to raise money for charity, Henry makes and sells three different sizes of T‑shirt, small, medium, and large. This year, the number of T‑shirts that
June 2023, AS Modelling with Algorithms, Q5 (9 marks): Four students, Jamal (J), Kai (K), Layla (L), and Mia (M) are planning to participate in a 200 m swimming relay race. Each of the four students must swim exactl
June 2022, Modelling with Algorithms, Q1 (7 marks): A 15 F H 3 D 24 20 34 I 17 B 8 15 25 14 25 10 E 24 J 12 C 39 G 29 K Fig. 1.1 The diagram in Fig. 1.1 represents a system of pipes through which a fluid can flow
June 2022, Modelling with Algorithms, Q6 (11 marks): Fig. 6.1 shows a weighted graph. The weights represent arc lengths. A 15 32 B 16 11 29 C 10 20 D 12 37 17 8 6 F E 16 7 G Fig. 6.1 (a) Apply Dijkstra’s algorithm
June 2022, Modelling with Algorithms, Q7 (15 marks): Kai makes three sizes of model car, small, medium and large, to sell each year at a fair. Kai has enough material to make either 250 small cars or 175 medium ca
June 2022, AS Modelling with Algorithms, Q5 (10 marks): Fig. 5.1 represents a system of pipes through which a fluid flows continuously from a source S to a sink T. The weight on the arcs show the capacities of the pi
June 2022, AS Modelling with Algorithms, Q6 (17 marks): Each Monday morning a company has its weekly delivery of milk. The milk comes in three types, whole, semi-skimmed and skimmed. The company manager knows that ea
November 2021, Modelling with Algorithms, Q4 (13 marks): Fig. 4.1 represents a system of pipes through which fluid can flow from a source, S, to a sink, T. It also shows two cuts, a and b. The arc weights show capacit
November 2021, Modelling with Algorithms, Q5 (19 marks): A mathematics competition consists of a written paper that involves questions on the topics of algebra, trigonometry, and calculus only. From experience of the
November 2021, AS Modelling with Algorithms, Q5 (16 marks): An LP formulation to find the shortest path from A to G in a directed network with seven vertices, A, B, …, G is given below. Minimise 15AB + 28AC + 31AD + 17BE
November 2021, AS Modelling with Algorithms, Q6 (14 marks): An incomplete initial tableau for a two-stage simplex solution for a maximisation integer linear programming (ILP) problem, in x, y and z where , , x y z 0 , is
November 2020, Modelling with Algorithms, Q3 (11 marks): a C G 80 45 60 A K 30 55 45 D H 50 45 25 55 25 L 35 20 65 I E 45 B 30 20 30 15 55 M 70 F J 75 a Fig. 3 The diagram in Fig. 3 represents a system of pipes throug
November 2020, Modelling with Algorithms, Q4 (13 marks): The following LP formulation can be used to find the minimum completion time, T, for the 11 activities A, B, …, K in a project. The durations of the activities
November 2020, AS Modelling with Algorithms, Q2 (6 marks): The fundraising committee at a school are planning a dance event. There must always be one teacher on duty throughout the event. The event is planned to last fo
November 2020, AS Modelling with Algorithms, Q7 (17 marks): The owner of a festival site is considering the number of each size of tent he is going to place in one of his fields before the summer tourist season begins. T
June 2019, Modelling with Algorithms, Q4 (11 marks): The table in Fig. 4.1 shows the unit cost, in hundreds of pounds, of transporting goods from each of four suppliers, A, B, C and D to each of three depots, X, Y
June 2019, Modelling with Algorithms, Q5 (15 marks): The initial tableau for a two-stage simplex solution for a maximisation LP problem is shown in Fig. 5.1. s1 s2 s3 s4 a1 a2 RHS Q P x y z 1 0 3 1 2 0 –1 –1 0 0 0
June 2019, AS Modelling with Algorithms, Q4 (13 marks): A D 17 G 22 53 24 15 E B 40 H 18 20 25 C I 30 F 27 Fig. 4.1 Fig. 4.1 shows a network representing a system of pipes. Fluid flows continuously from three sources
June 2018, AS Modelling with Algorithms, Q4 (10 marks): The table below shows the unit cost, in hundreds of pounds, of transporting goods from each of three suppliers, A, B and C to each of four depots, W, X, Y and Z

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