Lesson 4D.1.3

4D.1.3 Transportation problems as linear programs Quiz: Pearson Edexcel Further Maths, Unit 40

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4D.1.3, Transportation problems as linear programs: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 40: Transportation problems, written with Revision Ninja.

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The 20 questions

  1. In a transportation linear programme, what does the decision variable x_ij represent?

    • Shipped units
    • Unit cost
    • Supply limit
    • Total profit

  2. What is the primary objective of a standard transportation linear programme?

    • Maximise total cost
    • Minimise total profit
    • Equate all supplies
    • Minimise total cost

  3. Which equation represents a source constraint in a transportation model?

    • Row sum equals zero
    • Column sum equals supply
    • Row sum equals supply
    • Column sum equals demand

  4. What condition must hold for a transportation problem to be balanced?

    • Costs equal profits
    • Supply equals demand
    • Flows equal zero
    • Sources equal destinations

  5. How is an unbalanced transportation problem with excess supply made balanced?

    • Increase all demands
    • Add dummy destination
    • Add dummy source
    • Reduce total supply

  6. For a problem with 2 sources and 3 destinations, how many decision variables does the linear program have?

    • 5
    • 9
    • 3
    • 6

  7. Why does a balanced transportation problem contain a redundant constraint?

    • Equal total sums
    • Inconsistent supplies
    • Zero net demand
    • Negative costs

  8. How many independent constraints does a balanced transportation problem with 2 sources and 3 destinations have?

    • 5
    • 4
    • 3
    • 6

  9. Supplies are 20 and 30, and demands are 10, 25 and 15. What is the common total for this balanced problem?

    • 45
    • 55
    • 50
    • 60

  10. Total supply is 60 and total demand is 50. What is the demand of the dummy destination needed to balance the problem?

    • 5
    • 10
    • 15
    • 60

  11. How many decision variables does a transportation problem with 4 sources and 4 destinations have?

    • 8
    • 20
    • 12
    • 16

  12. A source A has supply 15 and source B has supply 25; destinations X and Y each need 20. Costs: A to X 2, A to Y 5, B to X 4, B to Y 1. What is the cost of the allocation A to X 15, B to X 5, B to Y 20?

    • 75
    • 65
    • 70
    • 90

  13. Given supplies A = 15, B = 25 and demands X = 20, Y = 20, what does x_BX + x_BY = 25 represent?

    • Destination Y demand
    • Source B supply
    • Source A supply
    • Destination X demand

  14. In the same example with supplies A = 15, B = 25 and demands X = 20, Y = 20, what is the demand constraint for destination X?

    • x_AY + x_BY = 20
    • x_AX + x_BX = 15
    • x_AX + x_BX = 20
    • x_AX + x_AY = 20

  15. In that same example, what is the total supply?

    • 40
    • 35
    • 50
    • 45

  16. Why are optimal transportation flows integer-valued when supplies and demands are integers?

    • Totally unimodular matrix
    • Symmetric cost matrix
    • Balanced total demand
    • Positive objective coefficients

  17. A non-degenerate basic feasible solution of a balanced 3 by 3 transportation problem has how many basic (occupied) variables?

    • 9
    • 5
    • 6
    • 3

  18. Why is the cost coefficient for a dummy destination set to zero in transportation problems?

    • Demand must be maximised
    • Costs are always negative
    • Surplus is not shipped
    • Supply equals zero

  19. What happens to the optimal allocation if every cost in one source row increases by 2?

    • Total supply increases
    • No change
    • Row cost doubles
    • Column values drop

  20. What do the non-negativity conditions x_ij >= 0 ensure in a transportation model?

    • Maximum capacity
    • Physical feasibility
    • Zero shipping cost
    • Integer values

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