Lesson 7.07a-d

7.07a-d Simplex tableaux and basic feasible solutions Quiz: OCR Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 7.07a-d, Simplex tableaux and basic feasible solutions: 20 multiple choice questions for the OCR Further Maths (H245), Unit 4: Discrete Mathematics (Y544), written with Revision Ninja.

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The 20 questions

  1. Which variable is added to transform a less-than-or-equal-to constraint into an equality?

    • Artificial variable
    • Decision variable
    • Surplus variable
    • Slack variable

  2. In a basic feasible solution, what value are the non-basic variables set equal to?

    • Their upper bound
    • Zero
    • The pivot value
    • One

  3. How is the pivot column chosen in a standard maximisation simplex tableau?

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

  4. How is the pivot row selected during an iteration of the simplex algorithm?

    • Minimum absolute ratio
    • Minimum positive ratio
    • Most negative ratio
    • Maximum positive ratio

  5. When does a standard maximisation simplex tableau reach an optimal solution?

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

  6. What geometric feature of a feasible region corresponds to a basic feasible solution?

    • Origin only
    • Vertex
    • Interior point
    • Bounding line

  7. If a problem has 3 constraints and 5 decision variables, how many basic variables exist?

    • 2
    • 8
    • 3
    • 5

  8. For 4 decision variables and 3 constraints, how many non-basic variables are there?

    • 4
    • 1
    • 7
    • 3

  9. What does an unbounded solution indicate during the ratio test in the simplex algorithm?

    • No positive entries
    • Zero right-hand side
    • No negative entries
    • Equal ratios

  10. What occurs when a tie arises for the minimum theta ratio in a simplex tableau?

    • Degeneracy
    • Unboundedness
    • Optimality
    • Infeasibility

  11. Which operations are performed on tableau rows to transform the pivot element to one?

    • Elementary row operations
    • Determinant multiplications
    • Matrix inversions
    • Column transformations

  12. In an initial simplex tableau, which variables form the starting basic feasible solution?

    • Decision variables
    • Objective variables
    • Slack variables
    • Surplus variables

  13. What name is given to the ratio of the right-hand side to pivot column entries?

    • Shadow value
    • Slack ratio
    • Pivot index
    • Theta ratio

  14. What entry value must the pivot element itself be made into after pivoting?

    • One
    • Negative one
    • Zero
    • Infinity

  15. What value must non-pivot entries in the pivot column become after pivoting?

    • Negative one
    • Zero
    • One
    • The ratio value

  16. What variable type is subtracted to convert a greater-than-or-equal-to constraint into an equality?

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

  17. What do the final tableau values under the slack variable columns represent?

    • Pivot ratios
    • Shadow prices
    • Decision bounds
    • Slack values

  18. What is the maximum number of non-zero variables in a basic feasible solution with m constraints?

    • m - n
    • n
    • m + n
    • m

  19. What column contains the current values of the basic variables in a simplex tableau?

    • Slack column
    • Right-hand side
    • Pivot column
    • Objective column

  20. What is the coefficient of any basic variable in the objective row of a simplex tableau?

    • Positive
    • Zero
    • Minus one
    • One

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