4D.1.1-4D.1.2 Initial solutions and the stepping-stone method Quiz: Pearson Edexcel Further Maths, Unit 40

The 20 questions

1. What is the north-west corner method used to find in a transportation problem?

   • Initial feasible solution
   • Shadow cost values
   • Improvement indices
   • Optimal total cost

2. Which cell is allocated first when using the north-west corner method?

   • Lowest cost cell
   • Highest cost cell
   • Top-left cell
   • Bottom-right cell

3. In the north-west corner method, what limits the allocation quantity in a selected cell?

   • Number of rows
   • Row index value
   • Remaining supply or demand
   • Total matrix cost

4. How many occupied cells indicate a degenerate solution in an m by n transportation problem?

   • Equal to m times n
   • Exactly m + n - 1
   • Greater than m + n - 1
   • Fewer than m + n - 1

5. How many occupied cells does a non-degenerate basic solution of a 3 by 4 transportation problem need?

   • 5
   • 7
   • 12
   • 6

6. In the stepping-stone method, what does the improvement index of an unoccupied cell measure?

   • Maximum supply limit
   • Minimum demand bound
   • Cost change per unit
   • Total routing flow

7. What starting value is conventionally assigned to row variable R1 in shadow cost calculations?

   • One
   • Total supply
   • Zero
   • Minus one

8. The north-west corner solution for supplies A = 20, B = 30, demands P = 10, Q = 25, R = 15, with costs A: 4, 6, 8 and B: 5, 3, 7, allocates AP = 10, AQ = 10, BQ = 15 and BR = 15. What is its total cost?

   • 260
   • 230
   • 240
   • 250

9. A two by three transportation table has four occupied cells. Is it degenerate?

   • Degenerate solution
   • Unbounded solution
   • Infeasible solution
   • Not degenerate

10. For the same north-west corner solution with R_A = 0, what is the shadow cost R_B for row B?

    • 5
    • 3
    • -5
    • -3

11. In the same solution, what is the improvement index of unoccupied cell A-R (cost 8)?

    • -2
    • 0
    • -10
    • 2

12. Which cell should enter the solution next in that solution, if the aim is to reduce cost?

    • Row B, column Q
    • Row A, column R
    • Row A, column P
    • Row B, column P

13. Using the stepping-stone loop for cell A-R, what is the largest amount θ that can be moved around the loop?

    • 15
    • 20
    • 10
    • 5

14. After one improvement from A-R with θ = 10, which cell leaves the solution?

    • Row A, column P
    • Row A, column Q
    • Row B, column Q
    • Row B, column R

15. What is the total cost after the improvement from A-R with θ = 10?

    • 230
    • 260
    • 240
    • 220

16. A three by three transportation table has only four occupied cells. What must be added?

    • Negative cost
    • Dummy destination
    • Zero-valued allocation
    • Artificial variable

17. Why must the stepping-stone loop alternate between plus and minus cells?

    • Maximise total flow
    • Keep totals unchanged
    • Satisfy cell demands
    • Minimise unit cost

18. Which unoccupied cell enters the solution in a minimising transportation problem?

    • Most negative index
    • Largest positive index
    • Zero improvement index
    • Smallest cost coefficient

19. After the single improvement (AP = 10, AR = 10, BQ = 25, BR = 5), what is the improvement index of cell A-Q?

    • 0
    • -2
    • 4
    • 2

20. What indicates that a transportation solution is optimal for minimisation?

    • All indices zero
    • Non-negative indices
    • Negative allocation values
    • All costs positive

Related quizzes

• Transportation problems as linear programs Quiz · 4D.1.3 · 20 questions
• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions
• Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions