For any activity with duration D, the standard CPM timing relations are: EF = ES + D, LS = LF - D, LF = LS + D, and D = EF - ES—hence, all the listed relations hold good.
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AEF = ES + D
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BLS = LF - D
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CLF = LS + D
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DD = EF - ES
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Eall the above
Answer
Correct Answer: all the above
Explanation
Introduction / Context:Forward and backward pass computations in CPM produce earliest and latest times. Consistency relations link these times to activity duration D.
Given Data / Assumptions:
- Activity duration = D.
- Earliest start/finish: ES, EF; Latest start/finish: LS, LF.
Concept / Approach:By definition, EF equals ES plus D. Similarly, during the backward pass, LS equals LF minus D. Rearranging gives LF = LS + D and D = EF - ES. These equalities are fundamental identities used in CPM calculations and float derivations.
Step-by-Step Solution:1) Forward pass: EF = ES + D.2) Backward pass: LS = LF - D.3) Rearrangement: LF = LS + D.4) From forward pass: D = EF - ES.
Verification / Alternative check:Test with a sample duration D = 5 units: if ES = 10, then EF = 15; if LF = 22, then LS = 17; all identities check out numerically.
Why Other Options Are Wrong:
- Each of A–D is correct; hence the comprehensive selection is required.
Common Pitfalls:
- Mixing earliest and latest columns when computing floats.
- Incorrectly applying calendars or lags without adjusting formulas.
Final Answer:all the above.