ITPEC FE Morning October 2022 Question 79
ITPEC FE Morning October 2022 — Question 79 of 80
For each purchasing quantity N, compute the expected profit using:E = Σ [ P(sold=k) × (min(k,N) × profit_per_unit - max(N-k,0) × disposal_loss) ]
- •Purchased 4: E = 1.0 × 40 = $40.0
- •Purchased 5: E = 0.3×37 + 0.7×50 = $46.1
- •Purchased 6: E = 0.3×34 + 0.3×47 + 0.4×60 = $48.3 ← maximum
- •Purchased 7: E = 0.3×31 + 0.3×44 + 0.3×57 + 0.1×70 = $46.6
Why not others:
- (a) 4 — guaranteed but lowest expected profit; no upside risk taken
- (b) 5 — better than 4, but disposing only 1 unit at 30% limits potential
- (d) 7 — higher ceiling but the 10% chance of selling 7 doesn't compensate for 30% chance of disposing 3 units at -$3 each
Key rule: Calculate expected profit for each option by weighting each scenario's (revenue - disposal cost) by its probability; pick the quantity with the highest total.
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