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

The 20 questions

1. The feasible region in a graphical linear programme is bounded by

   • the constraint lines and the non-negativity axes
   • the objective line only
   • a parabola
   • the coordinate axes only

2. The optimal solution of a linear programme occurs at

   • the origin always
   • the centre of the region
   • a vertex (corner point) of the feasible region
   • any interior point

3. In the objective line method, the objective line is moved

   • rotated about the origin
   • parallel to itself across the feasible region
   • only through the origin
   • perpendicular to the region

4. In the vertex method, for a maximisation, you evaluate the objective at each vertex and

   • take the average of the values
   • use the origin
   • choose the smallest value
   • choose the largest value

5. When integer solutions are required, the vertex method may need

   • ignoring the constraints
   • using only the origin
   • checking integer points near the optimal vertex
   • rounding the objective function

6. The feasible region of a linear programme is always

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

7. If the objective line is parallel to an edge of the feasible region, then

   • the problem is infeasible
   • the optimum is at the origin
   • there is no optimum
   • every point on that edge gives the optimum, so there are many optima

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. Objective P = 2x + 4y and constraint x + 2y <= 8 have parallel boundary slopes. What happens?

    • the optimum is unique at (8, 0)
    • there is no optimum
    • every point on the edge x + 2y = 8 between its two vertices is optimal
    • the optimum is at the origin

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 the vertex method fail when integer solutions are required?

    • the integer optimum can lie strictly inside the region, away from every vertex
    • objective lines have no slope
    • vertices are never integers
    • integer problems have no feasible region

18. Constraints x + y >= 6 and x + y <= 4 are imposed together. What does an empty feasible region mean?

    • the problem has no feasible solution
    • the optimum is at the origin
    • the objective is zero
    • there are infinitely many solutions

19. Maximise x + y subject to x - y <= 2 and x, y >= 0. What happens?

    • the optimum is at (1, 1)
    • the optimum is at (2, 0)
    • the optimum is at the origin
    • the objective is unbounded above

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)

Related quizzes

• Formulating linear programs Quiz · 3D.5.1 · 20 questions
• The Simplex algorithm for maximising and minimising Quiz · 3D.5.3 · 20 questions
• Two-stage Simplex and big-M methods Quiz · 3D.5.4 · 20 questions
• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions