Lesson 3D.5.2

3D.5.2 Graphical solution of two variable problems Quiz: Pearson Edexcel Further Maths, Unit 39

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3D.5.2, Graphical solution of two variable problems: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 39: Linear programming, written with Revision Ninja.

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The 20 questions

  1. What defines the boundary of a feasible region in linear programming?

    • Constraints and axes
    • Objective lines only
    • Vertices only
    • Optimal gradients

  2. Where on a bounded feasible region does an optimal solution occur?

    • Along an axis
    • At the origin
    • At a vertex
    • At the centre

  3. How is the objective line moved across the feasible region to find an optimum?

    • Perpendicularly
    • Parallel to itself
    • Towards the axes
    • Around the origin

  4. In the vertex method for a maximisation problem, which vertex value is chosen?

    • The mean value
    • The non-zero value
    • The smallest value
    • The largest value

  5. When integer solutions are required, what must be tested near the optimal vertex?

    • Boundary midpoints
    • Fractional vertices
    • Nearby integer points
    • Non-feasible points

  6. The feasible region of a linear programme is always

    • a non-convex star shape
    • a convex region
    • a single point
    • a circle

  7. What exists if the objective line is parallel to an edge of the feasible region?

    • A single optimum
    • An unbounded region
    • No optimal solution
    • Multiple optimal solutions

  8. Maximise P = 3x + 2y subject to x + y <= 4, x >= 0 and y >= 0. What is the maximum value of P?

    • 4
    • 8
    • 12
    • 16

  9. With constraints 2x + y <= 10, x + 2y <= 8 and x, y >= 0, maximise P = x + y. What is the maximum and where is it?

    • 4 at (0, 4)
    • 5 at (5, 0)
    • 6 at (4, 2)
    • 7 at (3, 3)

  10. Where do the lines 2x + y = 10 and x + 2y = 8 meet?

    • (4, 2)
    • (3, 4)
    • (2, 4)
    • (5, 0)

  11. The linear programme optimum with an integer requirement lies at (2.5, 1.5). Which integer points should be checked first?

    • (2.5, 1.5) only
    • (0, 0) and (5, 3)
    • (2, 3) and (3, 2)
    • (2, 1), (2, 2), (3, 1) and (3, 2)

  12. If an objective line is parallel to a boundary constraint line, which points are optimal?

    • Only one vertex
    • Only integer points
    • All edge points
    • No region points

  13. Minimise C = 2x + y subject to x + y >= 4 and x, y >= 0. What is the minimum?

    • 8 at (4, 0)
    • 4 at (0, 4)
    • 0 at (0, 0)
    • 6 at (2, 2)

  14. Maximise P = 5x + 2y over a region with vertices (0, 0), (6, 0), (2, 5) and (0, 4). What is the maximum?

    • 20
    • 8
    • 30
    • 24

  15. The feasible region is x >= 1, y >= 2 and x + y <= 6. What is the maximum value of x?

    • 1
    • 5
    • 4
    • 6

  16. Maximise P = 3x + y with 2x + y <= 10, x + 2y <= 8 and x, y >= 0. What is the maximum?

    • 15 at (5, 0)
    • 16 at (4, 2)
    • 4 at (0, 4)
    • 14 at (4, 2)

  17. Why can testing only vertices fail when finding an integer optimal solution?

    • Optimum inside region
    • No feasible region
    • Vertices are integers
    • Constraints are nonlinear

  18. What type of solution exists if a linear programme has an empty feasible region?

    • No feasible solution
    • An unbounded solution
    • A unique vertex
    • Multiple optimal solutions

  19. What is a linear programme called if its objective value can increase indefinitely?

    • Degenerate
    • Infeasible
    • Multiple optimal
    • Unbounded

  20. Maximise P = 4x + 3y subject to x + y <= 10, 2x + y <= 14 and x, y >= 0. What is the maximum?

    • 30 at (0, 10)
    • 34 at (4, 6)
    • 28 at (7, 0)
    • 36 at (6, 4)

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