7.07e Iterations of the simplex algorithm and its graphical interpretation Quiz: OCR Further Maths, Unit 4

The 20 questions

1. In a simplex tableau, what characterises a column corresponding to a basic variable?

   • All zeros
   • All ones
   • Two ones
   • One 1 and zeros

2. Graphically, what does a single iteration of the simplex algorithm represent?

   • Crossing boundary
   • Reflecting across axis
   • Jumping to centre
   • Moving along edge

3. Graphically, what do the vertices of a feasible region represent in the simplex algorithm?

   • Non-basic solutions
   • Infeasible solutions
   • Unbounded solutions
   • Basic feasible solutions

4. In a simplex problem, what value do non-basic variables take at a basic solution?

   • One
   • Objective value
   • Pivot value
   • Zero

5. What geometric shape is formed by the set of all feasible solutions in linear programming?

   • Circle
   • Concave polygon
   • Curved surface
   • Convex polygon

6. In the simplex algorithm for maximisation, when is the optimal solution reached?

   • No negative indicators
   • All variables basic
   • Objective row zero
   • All entries positive

7. What defines a zero-sum game in game theory?

   • Zero total payoff
   • No pure strategies
   • Row player wins
   • All payoffs positive

8. In a standard payoff matrix, what do positive entries usually represent?

   • Probability of winning
   • Column player gain
   • Row player loss
   • Row player gain

9. For the row player, how is a dominated row identified in a payoff matrix?

   • All entries smaller
   • Entries are equal
   • All entries larger
   • Sum is zero

10. For the column player, which column is dominated and can be removed?

    • Larger entry column
    • Smaller entry column
    • Zero sum column
    • Negative entry column

11. Which rule determines the play-safe strategy for players in a matrix game?

    • Maximin or minimax
    • Maximum payoff
    • Dominant column only
    • Random choice

12. What condition indicates that a zero-sum game has a stable solution?

    • Maximin equals minimax
    • All entries equal
    • Maximin exceeds minimax
    • Payoffs sum zero

13. What is another term for a stable solution in a two-player zero-sum game?

    • Pivot point
    • Critical point
    • Saddle point
    • Turning point

14. What defines a Nash Equilibrium in terms of individual player choices?

    • Zero payoff sum
    • No incentive to deviate
    • Both players win equal
    • Randomised strategy choice

15. When must a player use a mixed strategy rather than a pure strategy?

    • Only two options
    • All payoffs positive
    • Matrix is square
    • No stable solution

16. Graphically, how does the row player find the optimal probability in a 2xn game?

    • Midpoint of axis
    • Lowest intersection point
    • Origin
    • Highest intersection point

17. During a simplex iteration, how is the pivot row selected?

    • Smallest negative entry
    • Absolute largest value
    • Largest positive entry
    • Smallest positive ratio

18. For a game with no saddle point, where does the optimal probability p lie?

    • At 0 or 1
    • Always equal to 0.5
    • Greater than 1
    • Between 0 and 1

19. In the simplex algorithm, how is the pivot column chosen for a maximisation problem?

    • Most negative indicator
    • Smallest positive ratio
    • Largest positive ratio
    • Most positive indicator

20. What type of strategy involves a player deterministically choosing a single action every time?

    • Play-safe strategy
    • Pure strategy
    • Mixed strategy
    • Dominant strategy

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