Hungarian algorithm as a linear programme

Hungarian algorithm as a linear programme Quiz

Spec 2.2 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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1. How many variables $x_{ij}$ are there in a $3\times3$ assignment problem?
- A. $3$
- B. $6$
- C. $9$
- D. $27$
2. Which constraint says worker 2 does exactly one of three tasks?
- A. $x_{21}+x_{22}+x_{23}=1$
- B. $x_{12}+x_{22}+x_{32}=1$
- C. $x_{21}+x_{22}+x_{23}\le1$
- D. $x_{21}x_{22}x_{23}=1$
3. Costs are $4, 7$ for worker 1 and $5, 3$ for worker 2 (tasks 1, 2). What is the objective to minimise?
- A. $4x_{11}+5x_{12}+7x_{21}+3x_{22}$
- B. $x_{11}+x_{12}+x_{21}+x_{22}$
- C. $4+7+5+3$
- D. $4x_{11}+7x_{12}+5x_{21}+3x_{22}$
4. Five workers and three tasks. What constraint is used for each worker?
- A. Exactly one task ( $=1$ )
- B. At most one task ( $\le1$ )
- C. At least one task ( $\ge1$ )
- D. No constraint is needed
5. What does the constraint $x_{11}+x_{22}\le1$ say?
- A. Both pairings must be used
- B. Neither pairing may be used
- C. They cannot both be used
- D. Exactly one must be used