plumiLinear programming: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on D.4 Linear programming, 2018–2025, with its mark scheme and examiner’s report.
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All 38 questions on Linear programming, 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, Modelling with Algorithms, Q4 (10 marks): The following LP problem in x, y and z is as follows. Maximise P 2 x y 4 z = + + Subject to x 3 y z 40 - + G 3 x y z 56 + + G 2 x 4 y z k - + + G x 0 , y 0 , z
- June 2025, Modelling with Algorithms, Q6 (14 marks): An incomplete initial tableau for a two-stage simplex solution for a maximisation linear programming problem, in x, y and z where , x y z , 0 , is shown below.
- 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, Q6 (11 marks): Consider the following LP problem in X and Y. Maximise Q 8 X 9 Y = - + Subject to 5 X 6 Y 87 - + G 2 X Y 6 + G 3 X Y 16 - - G X 2 , Y 0 - G H (a) Explain why th
- 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, Modelling with Algorithms, Q3 (11 marks): A directed network consists of eight nodes, A–H, and fifteen arcs. A shortest path from A to H needs to be found for this network. The objective for an LP formu
- June 2023, Modelling with Algorithms, Q4 (7 marks): y 2y = 5x 2y = x + k R x +2y = 36 x O The diagram shows the constraints of a linear programming problem in which the objective is to maximise P x ky , where k i
- June 2023, Modelling with Algorithms, Q6 (15 marks): The initial simplex tableau for a maximisation LP problem is shown in Fig. 6.1. Fig. 6.1 P x y z s1 s2 s3 RHS 1 2 1 3 0 0 0 0 - - - b 0 1 2 1 1 0 0 - 0 0 2 0 1
- 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 2023, AS Modelling with Algorithms, Q6 (13 marks): Fig. 6.1 y 2 y 5 x = 13 12 11 3 y 2 x = 10 9 8 7 6 5 4 3 R 2 1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 x y x y 3 2 20 2 12 + = + = Fig. 6.1 shows the constraint
- 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, Q5 (10 marks): Consider the following LP problem. Maximise P 2 x 3 y z = + - Subject to 3 x y 4 z 70 + - G 5 x 4 y 60 + G x 4 , y 2 , z 2 H H G - (a) Explain why the simplex a
- 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, Q3 (7 marks): The following LP problem in x, y and z is as follows. Minimise P x 2 y z =- - + subject to 2 x 3 y z 45 - + + G x y 2 z 50 - - G x y 3 z 25 - + + G x y z , , 0
- 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, Modelling with Algorithms, Q5 (19 marks): y k (1,k) (3,2) R 1 0.5 x 0.75 1 5 Fig. 5.1 Fig. 5.1 shows the constraints of a linear programming problem, in which the objective is to maximise a function of
- 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 2019, AS Modelling with Algorithms, Q5 (17 marks): An LP problem in x, y and z is formulated as follows. Maximise P 3 x 2 y 5 z = + + subject to x y z 26 + + H 2 x y z 34 + + G 2 x z 10 - = x y z , , 0 H (a) • C
- 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
- June 2018, AS Modelling with Algorithms, Q6 (17 marks): The following LP problem is to be solved. P x y z Maximise 3 2 = + + x y subject to 2 30 + G 2 x y z 14 + + H 2 x z 20 + G x y z , , 0 H (i) • Complete the init
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