Lesson 7.06a-b

7.06a-b Formulating linear programming problems and slack variables Quiz: OCR Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson 7.06a-b, Formulating linear programming problems and slack variables: 20 multiple choice questions for the OCR Further Maths (H245), Unit 4: Discrete Mathematics (Y544), written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. What type of function represents the quantity to be maximised or minimised in linear programming?

    • Constraint function
    • Slack function
    • Feasible function
    • Objective function

  2. What mathematical term describes the unknown quantities that a decision maker needs to determine?

    • Decision variables
    • Slack variables
    • Bound parameters
    • Objective constants

  3. Why are non-negativity constraints included in linear programming models?

    • Costs are zero
    • Slack must vanish
    • Quantities are non-negative
    • Profits are fixed

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

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

  5. What value does a slack variable take when a constraint is binding?

    • Negative one
    • Less than zero
    • Greater than zero
    • Zero

  6. What value does a slack variable take when a constraint is non-binding?

    • Less than zero
    • Greater than zero
    • Equal to zero
    • Negative one

  7. Which inequality restriction must always apply to any slack variable s?

    • s > 1
    • s <= 0
    • s >= 0
    • s = 0

  8. How is the constraint 2x + 3y <= 12 written using a slack variable s?

    • 2x + 3y + s <= 12
    • 2x + 3y = 12 + s
    • 2x + 3y + s = 12
    • 2x + 3y - s = 12

  9. How many slack variables are needed for a problem with four less-than-or-equal-to constraints?

    • 1
    • 2
    • 4
    • 8

  10. What term describes the set of all points that satisfy every constraint simultaneously?

    • Feasible region
    • Slack region
    • Optimal region
    • Objective region

  11. For the constraint x + 2y <= 20, what is the slack value at point (4, 5)?

    • 10
    • 14
    • 6
    • 0

  12. For the constraint 3x + 4y <= 24, what is the slack value at point (4, 3)?

    • 0
    • 4
    • 12
    • 24

  13. If a constraint has a slack value of zero at a point, what is that constraint called?

    • Redundant constraint
    • Non-binding constraint
    • Binding constraint
    • Unbounded constraint

  14. How is the constraint 5x - y <= 15 expressed as an equation using slack variable s1?

    • 5x - y = 15 + s1
    • 5x - y + s1 = 15
    • 5x + s1 = 15 - y
    • 5x - y - s1 = 15

  15. What do constraints in a linear programming model represent?

    • Resource limitations
    • Profit goals
    • Variable costs
    • Optimal solutions

  16. In linear programming, what key condition must all expressions in constraints and objectives satisfy?

    • Integer expressions
    • Logarithmic expressions
    • Linear expressions
    • Quadratic expressions

  17. For x + 3y <= 18, what is the value of slack variable s at point (3, 4)?

    • 15
    • 6
    • 0
    • 3

  18. If a point lies outside the feasible region, how is that point described?

    • Slack point
    • Infeasible point
    • Binding point
    • Optimal point

  19. For the constraint 4x + y <= 40, what is the slack variable value at point (5, 10)?

    • 10
    • 30
    • 20
    • 0

  20. What type of variable is subtracted to transform a greater-than-or-equal-to constraint into an equality?

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

All OCR Further Maths quizzes