Lesson 7.06c-e

7.06c-e Graphical solutions and the effect of changing constraints Quiz: OCR Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 7.06c-e, Graphical solutions and the effect of changing constraints: 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. What is the region containing all points that satisfy every constraint in linear programming?

    • Feasible region
    • Bounded region
    • Optimal region
    • Objective region

  2. Which term describes a constraint that passes directly through the optimal solution point?

    • Non-binding constraint
    • Slack constraint
    • Redundant constraint
    • Binding constraint

  3. What is the extra value remaining when a less-than-or-equal constraint is not fully used?

    • Gradient
    • Shadow price
    • Slack
    • Surplus

  4. What is the amount by which a greater-than-or-equal constraint exceeds its required minimum?

    • Slack
    • Surplus
    • Margin
    • Optimal value

  5. What happens to the optimal maximum value if a redundant constraint is removed?

    • Decreases
    • Increases
    • Stays the same
    • Becomes zero

  6. What is a constraint called if its removal does not alter the feasible region?

    • Feasible
    • Binding
    • Redundant
    • Critical

  7. Where must the optimal solution to a linear programming problem always lie?

    • Outside the region
    • At a vertex
    • At the origin
    • Along the axis

  8. What line is moved parallel across the feasible region to find the maximum point?

    • Constraint line
    • Objective line
    • Boundary line
    • Feasible line

  9. In a maximisation problem, what effect does adding a new constraint usually have on maximum profit?

    • Becomes negative
    • Always doubles
    • Always increases
    • Decreases or unchanges

  10. If a binding constraint's RHS increases by 1 unit, what represents the increase in optimal value?

    • Surplus value
    • Slack value
    • Gradient
    • Shadow price

  11. A point (3, 4) lies in the feasible region for x + 2y <= 12. What is the slack?

    • 11
    • 1
    • 2
    • 0

  12. Point (5, 2) satisfies 2x + y >= 8. What is the surplus for this constraint?

    • 0
    • 8
    • 4
    • 2

  13. Objective function P = 3x + 2y. What is the gradient of the objective lines?

    • -1.5
    • 0.67
    • -0.67
    • 1.5

  14. If non-binding constraint x + y <= 10 has slack 3, what is its current LHS value?

    • 3
    • 13
    • 10
    • 7

  15. What geometric change occurs to a constraint line ax + by <= c when c increases?

    • Rotates anti-clockwise
    • Parallel shift inwards
    • Rotates clockwise
    • Parallel shift outwards

  16. What is the shadow price of a non-binding constraint in a maximisation problem?

    • Positive
    • Negative
    • One
    • Zero

  17. Maximise P = x + y subject to x + 2y <= 6 and 2x + y <= 6. What is maximum P?

    • 6
    • 5
    • 4
    • 3

  18. An optimal solution is (2.4, 3.8). If variables must be integers, which method finds the integer optimum?

    • Simple rounding up
    • Testing nearby grid points
    • Simple rounding down
    • Doubling all constraints

  19. Relaxing a constraint means changing x + y <= 5 to which of the following?

    • x + y >= 5
    • x + y <= 4
    • x + y <= 6
    • 2x + 2y <= 5

  20. What happens to the feasible region when a non-redundant constraint is tightened?

    • It stays identical
    • It disappears completely
    • It shrinks
    • It expands

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