The simplex algorithm: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 4.3 The simplex algorithm, 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 17 questions on The simplex algorithm, as a list

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, 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, 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 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, 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, 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, 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, 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, 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, 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, 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, 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, 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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