DD3-DD4 The Simplex algorithm Quiz: AQA Further Maths, Unit 5

The 20 questions

1. What variable is added to a ≤ inequality to convert it into an equation for Simplex?

   • Surplus variable
   • Basic variable
   • Slack variable
   • Artificial variable

2. When maximising in Simplex, which objective row coefficient indicates the entering variable?

   • Smallest positive
   • Largest positive
   • Most positive
   • Most negative

3. In the Simplex algorithm, how is the leaving variable selected?

   • Smallest positive ratio
   • Most negative coefficient
   • Most negative ratio
   • Largest positive ratio

4. Maximise P = 5x + 4y subject to 6x + 4y ≤ 24 and x + 2y ≤ 6, with x ≥ 0 and y ≥ 0. In the initial tableau with slack variables s1 and s2, what are the values of s1 and s2 when x = y = 0?

   • s1 = 6 and s2 = 24, with P = 0
   • s1 = 4 and s2 = 6, with P = 5
   • s1 = 24 and s2 = 6, with P = 0
   • s1 = 0 and s2 = 0, with P = 24

5. For objective P = 5x + 4y, which variable enters the basis first in Simplex?

   • x
   • y
   • s1
   • s2

6. For constraints 6x + 4y ≤ 24 and x + 2y ≤ 6, which row leaves when x enters?

   • Objective row
   • s1 row
   • y row
   • s2 row

7. Maximise P = 5x + 4y subject to 6x + 4y ≤ 24 and x + 2y ≤ 6, with x ≥ 0 and y ≥ 0. After the first pivot, x = 4 - (2/3)y - (1/6)s1. What is the value of x when y = 0 and s1 = 0?

   • 3
   • 24
   • 4
   • 6

8. Maximise P = 5x + 4y subject to 6x + 4y ≤ 24 and x + 2y ≤ 6, with x ≥ 0 and y ≥ 0. What is the optimal value of P?

   • 24
   • 21
   • 18
   • 20

9. Maximise P = 5x + 4y subject to 6x + 4y ≤ 24 and x + 2y ≤ 6, with x ≥ 0 and y ≥ 0. At which point (x, y) is the optimum reached?

   • (2.4, 1.8)
   • (3, 1.5)
   • (4, 0)
   • (0, 3)

10. At optimum (3, 1.5) for 6x + 4y ≤ 24 and x + 2y ≤ 6, which constraints are binding?

    • Second constraint only
    • First constraint only
    • Both constraints
    • Neither constraint

11. What is the value of slack variable s1 at the optimal point (3, 1.5) for 6x + 4y ≤ 24?

    • 24
    • 6
    • 0
    • 4

12. In a maximisation Simplex tableau, when is the optimal solution reached?

    • No positive coefficients
    • All zero pivot values
    • No negative coefficients
    • Maximum basic variables

13. What does a pivot column with no positive entries indicate in the Simplex method?

    • No feasible solution
    • Unbounded solution
    • Multiple optimal solutions
    • Degenerate solution

14. What is the main purpose of adding slack variables to ≤ constraints in Simplex?

    • Remove non-negativity
    • Double the variables
    • Eliminate objective function
    • Convert to equations

15. If a slack variable is zero at the optimal solution, what type of constraint is it?

    • Unbounded
    • Non-binding
    • Binding
    • Infeasible

16. A maximisation problem has three ≤ constraints and two decision variables. How many slack variables are introduced?

    • 2
    • 5
    • 1
    • 3

17. In a Simplex tableau, pivot column entries are 2 and -1 with RHS 8 and 4. Which row leaves?

    • Both rows
    • Neither row
    • Second row
    • First row

18. In a Simplex objective row P - 3x - 2y = 0, what does -3 for x mean?

    • Increases by 3
    • Increases by 1
    • Decreases by 3
    • Decreases by 1

19. Where does each pivot step in the Simplex algorithm move across the feasible region?

    • Adjacent vertex
    • Random vertex
    • Feasible region centre
    • Opposite vertex

20. An optimal Simplex objective row has a non-basic variable with coefficient 0. What does this indicate?

    • No feasible solution
    • Unique optimal solution
    • An unbounded solution
    • Alternative optimal solutions

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