Moderate -0.5 This appears to be a single row from a distance matrix in Floyd's algorithm, requiring students to apply a standard algorithmic procedure. While Floyd's algorithm involves systematic iteration, this is a routine application of a learned technique with clear mechanical steps, making it easier than average but not trivial since it requires careful bookkeeping and understanding of the algorithm's logic.
Decision tree with three decision nodes (retire now at 59, at 60, at 65) and chance nodes for part-time probability at each stage
B1 B1 B1 B1
B1 for correct structure; B1 for correct probabilities; B1 for correct monetary values on branches; B1 for fully correct tree
Part (ii)
Answer
Marks
Guidance
Pension calculations and EMV for each scenario computed; e.g. retire now: pension \(= \frac{35}{80} \times 50000 \times 11\); part-time earnings added probabilistically; EMVs compared to find optimal
M1 M1 M1 A1 A1 A1 A1 A1 A1
Method marks for correct pension formula, correct part-time earnings, correct EMV calculation; accuracy marks for correct values
Part (iii)
Answer
Marks
Guidance
Utility computed as gross income \(\times 3^{-p}\) for each scenario; expected utilities calculated and compared; optimal decision stated
M1 M1 M1 A1 A1 A1 A1
M marks for method; A marks for correct values and conclusion
# Question 3:
## Part (i)
| Decision tree with three decision nodes (retire now at 59, at 60, at 65) and chance nodes for part-time probability at each stage | B1 B1 B1 B1 | B1 for correct structure; B1 for correct probabilities; B1 for correct monetary values on branches; B1 for fully correct tree |
## Part (ii)
| Pension calculations and EMV for each scenario computed; e.g. retire now: pension $= \frac{35}{80} \times 50000 \times 11$; part-time earnings added probabilistically; EMVs compared to find optimal | M1 M1 M1 A1 A1 A1 A1 A1 A1 | Method marks for correct pension formula, correct part-time earnings, correct EMV calculation; accuracy marks for correct values |
## Part (iii)
| Utility computed as gross income $\times 3^{-p}$ for each scenario; expected utilities calculated and compared; optimal decision stated | M1 M1 M1 A1 A1 A1 A1 | M marks for method; A marks for correct values and conclusion |
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