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Question 1
ప్రశ్న 1
In CPM time-cost trade-off analysis, which statement correctly distinguishes NORMAL and CRASH activity conditions?
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Explanation:
The normal operating mode is generally the activity execution method with the least direct cost. Its corresponding duration is called normal time. The crash duration is the shortest technically achievable duration under the available alternatives. Its associated direct cost is termed crash cost. Extra resources or more expensive methods commonly make the crash cost greater than normal cost. Neither duration should be confused with activity float or a guaranteed project-level completion date.
వివరణ:
Question 2
ప్రశ్న 2
For a pipeline activity, normal time is 10 days at a direct cost of ₹80 lakh and crash time is 6 days at ₹104 lakh. Assuming a linear time-cost relationship, what is its cost slope?
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Explanation:
The permissible duration reduction is 10 - 6 = 4 days. The incremental direct cost from normal to crash conditions is ₹104 - ₹80 = ₹24 lakh. Cost slope divides the extra cost by the available duration reduction. It is therefore ₹24/4 = ₹6 lakh per day. This slope applies to intermediate durations only under the stated linear assumption. It is not the average daily normal cost of the activity.
వివరణ:
Question 3
ప్రశ్న 3
An activity has normal time 9 days at ₹25 lakh and crash time 5 days at ₹41 lakh. Under linear interpolation, what direct activity cost corresponds to an adopted duration of 7 days?
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Explanation:
The available reduction from normal to crash time is four days. The total increase in direct cost is ₹16 lakh, giving a slope of ₹4 lakh per day. A seven-day execution plan saves two days relative to the normal duration. Its added direct cost is therefore 2 × ₹4 = ₹8 lakh. Adding this amount to the normal cost gives ₹25 + ₹8 = ₹33 lakh. The calculation requires a linear activity time-cost relationship.
వివరణ:
Question 4
ప్రశ్న 4
A shaft-construction activity has a normal duration of 14 days and a verified minimum crash duration of 10 days. The project engineer proposes a 9-day duration without changing the technical method or feasibility limits. Which assessment is correct?
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Explanation:
Crash time represents the minimum feasible activity duration within the defined alternatives. Here that lower bound is ten days. The greatest permissible reduction from the normal duration is four days. A requested nine-day duration exceeds the stated feasible crashing range. Meeting it would require an independently justified change in the available methods or assumptions. Ordinary CPM arithmetic cannot override a technical feasibility limit.
వివరణ:
Question 5
ప్రశ్న 5
A single critical sequence contains A = 7 days, B = 6 days and C = 4 days. The available linear crash options are A: 1 day at ₹3 lakh/day; B: up to 2 days at ₹2 lakh/day; C: 1 day at ₹5 lakh/day. No other paths or resource constraints exist. Which is the least-cost FIRST one-day project reduction?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
All three activities lie on the only critical path. Shortening any one of them by one day will shorten the project by one day. The marginal direct costs are ₹3 lakh for A, ₹2 lakh for B and ₹5 lakh for C. B is the least expensive eligible activity and has two days of remaining crash capacity. Reducing B by one day changes project duration from 17 to 16 days. Its additional direct cost is only ₹2 lakh.
వివరణ:
Question 6
ప్రశ్న 6
A project has two independent required start-to-finish branches: A–C lasts 15 days and B–D lasts 12 days. B is crashable by 2 days at ₹2 lakh per day, whereas the 15-day branch is unchanged. If B is fully crashed, what happens to project duration and direct cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The original project duration is the longer of the two required branch durations, namely 15 days. The B–D branch initially lasts only 12 days. Shortening B by two days makes that branch last 10 days. The A–C branch still requires 15 days and remains controlling. The project therefore does not finish earlier. Crashing B nevertheless increases direct cost by 2 × ₹2 = ₹4 lakh.
వివరణ:
Question 7
ప్రశ్న 7
Two independent required CPM branches are A–C = 18 days and B–D = 16 days. Only A can be crashed on the longer branch, by up to 3 days at ₹2 lakh/day; B–D is initially unchanged. After crashing A by 2 days, what are the project duration, extra direct cost and critical-path condition?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The initial project completion is controlled by the 18-day A–C branch. Reducing A by two days shortens that branch to 16 days. The unchanged B–D branch also requires 16 days. Both branches now govern the common project finish. The extra direct cost is 2 × ₹2 = ₹4 lakh. Any further reduction in the project duration must address both controlling branches or an eligible shared activity.
వివరణ:
Question 8
ప్రశ్న 8
A CPM network has two critical branches A–C and B–D, each taking 9 days before a COMMON final activity E of 3 days. Available one-day crash slopes are A = ₹3 lakh, B = ₹4 lakh, E = ₹5 lakh; C and D cannot be crashed. Which plan reduces project duration from 12 to 11 days at minimum added direct cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Both branches take nine days to reach the common activity E. Crashing A alone leaves the B–D branch controlling the start of E. Crashing B alone similarly leaves the A–C branch controlling. Crashing both branch activities would save one project day but cost ₹3 + ₹4 = ₹7 lakh. Reducing the common final activity E by one day shortens both complete critical paths simultaneously. Its added direct cost is ₹5 lakh, making it the cheapest effective option.
వివరణ:
Question 9
ప్రశ్న 9
A project has exactly two DISJOINT critical paths, A–C and B–D, each lasting 12 days. Only A on the first path and B on the second can each be shortened by at least one day, at marginal costs of ₹2 lakh/day and ₹3 lakh/day respectively. What is the minimum extra direct cost to shorten project completion to 11 days?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Both disjoint paths control the initial 12-day project duration. Crashing A alone would leave B–D unchanged at 12 days. Crashing B alone would leave A–C unchanged at 12 days. To complete in eleven days, both paths must be shortened by at least one day. The stated least expensive eligible actions are one day on A and one day on B. Their combined marginal direct cost is ₹2 + ₹3 = ₹5 lakh.
వివరణ:
Question 10
ప్రశ్న 10
Two required parallel paths are A–C = 14 days and B–D = 12 days. C and D are fixed; A can be crashed by up to 3 days at ₹2 lakh/day, and B can be crashed by up to 1 day at ₹4 lakh/day. With linear costs and no other options, what MINIMUM additional direct cost achieves a project duration of 11 days?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The A–C branch initially controls the 14-day project finish. Reducing A by two days creates a tie at twelve days, costing ₹4 lakh. To reach eleven days, A must lose one further day and B–D must also be shortened by one day. The three-day reduction in A costs 3 × ₹2 = ₹6 lakh. The one-day reduction in B costs another ₹4 lakh. Thus the minimum extra direct cost is ₹10 lakh, and both final paths last eleven days.
వివరణ:
Question 11
ప్రశ్న 11
A project has two branches joining before a common activity E: A–C has normal times 6 and 5 days and minimum crash times 4 and 4 days; B–D has normal times 7 and 5 days and minimum crash times 5 and 3 days; E has normal time 3 days and crash time 2 days. Assume independent feasible reductions. What is the SHORTEST feasible project duration?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At normal durations, the two upstream branches take eleven and twelve days. The common final activity E adds three days, giving a normal project duration of fifteen days. At their feasible minimum durations, A–C takes 4 + 4 = 8 days. B–D takes 5 + 3 = 8 days. The common E can then take as little as two days. The minimum possible project completion is max(8, 8) + 2 = 10 days.
వివరణ:
Question 12
ప్రశ్న 12
A project consists only of two serial critical activities A and B. Their normal durations are 6 and 5 days, and their available reductions are A: 2 days at ₹3 lakh/day and B: 1 day at ₹5 lakh/day. The NORMAL total project direct cost is ₹84 lakh. If the project must be completed in 8 days instead of 11 days, what is the minimum total DIRECT cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The two serial activities initially take 6 + 5 = 11 days. An eight-day deadline requires a reduction of three days. A can supply at most two days, and B can supply at most one day. Therefore both activities must be fully crashed within their stated limits. The incremental direct cost is 2 × ₹3 + 1 × ₹5 = ₹11 lakh. The resulting direct cost is ₹84 + ₹11 = ₹95 lakh.
వివరణ:
Question 13
ప్రశ్న 13
An 18-day project has normal direct cost ₹120 lakh and time-related indirect cost ₹4 lakh per day. An effective crashing plan shortens completion to 16 days and adds ₹5 lakh of DIRECT cost for EACH day saved. With no other cost changes, what is the revised TOTAL project cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The original indirect cost is 18 × ₹4 = ₹72 lakh. Hence the original total cost is ₹120 + ₹72 = ₹192 lakh. Saving two days by the stated plan adds 2 × ₹5 = ₹10 lakh to direct cost. The revised direct cost is therefore ₹130 lakh. The revised indirect cost is 16 × ₹4 = ₹64 lakh. Total project cost becomes ₹130 + ₹64 = ₹194 lakh, which is ₹2 lakh higher.
వివరణ:
Question 14
ప్రశ్న 14
At the current CPM schedule, one feasible one-day project reduction increases direct cost by ₹1.5 lakh. Time-related site overhead is ₹2 lakh per project day, and no other costs change. What is the NET total-cost effect of this effective one-day crash?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A one-day reduction in project duration saves one day of site overhead. At ₹2 lakh per day, that indirect-cost saving is ₹2 lakh. The effective crash action costs an additional ₹1.5 lakh in direct expenditure. The net change in total project cost is ₹1.5 - ₹2 = -₹0.5 lakh. The negative sign indicates a saving of ₹0.5 lakh. This conclusion assumes the activity reduction genuinely shortens overall project completion.
వివరణ:
Question 15
ప్రశ్న 15
A SINGLE serial critical path consists of A = 7 days, B = 6 days and fixed C = 4 days. A can be shortened by 2 days at ₹1 lakh/day and B by 2 days at ₹3 lakh/day. Normal project direct cost is ₹50 lakh and time-related indirect cost is ₹2 lakh/day. With linear crash costs, what is the MINIMUM total cost and corresponding project duration?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The normal project duration is 7 + 6 + 4 = 17 days and its total cost is ₹50 + 17 × ₹2 = ₹84 lakh. Crashing A saves project days at a direct cost of ₹1 lakh per day against ₹2 lakh per day of overhead savings. Both available days of A should therefore be crashed, producing duration fifteen days and direct cost ₹52 lakh. Total cost at that point is ₹52 + 15 × ₹2 = ₹82 lakh. Additional crashing of B costs ₹3 lakh per day but saves only ₹2 lakh per day in overhead. Consequently further reduction increases total cost, making fifteen days the optimum under the stated choices.
వివరణ:
Question 16
ప్రశ్న 16
Two DISJOINT required critical branches each take 12 days, and no shared activity can be shortened. The cheapest effective one-day crash requires spending ₹2 lakh on the first branch AND ₹3 lakh on the second; each has exactly one crashable day. Normal project direct cost is ₹90 lakh and time-related indirect cost is ₹4 lakh/day. What is the minimum total project cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At normal duration, direct cost is ₹90 lakh and overhead is 12 × ₹4 = ₹48 lakh. Thus normal total cost is ₹138 lakh. One-day project reduction requires shortening both disjoint critical paths. That joint action increases direct cost by ₹2 + ₹3 = ₹5 lakh while overhead falls by only ₹4 lakh. The eleven-day alternative therefore costs ₹95 + ₹44 = ₹139 lakh. No further reductions are available, so the minimum cost is ₹138 lakh at twelve days.
వివరణ:
Question 17
ప్రశ్న 17
A project has two DISJOINT required paths of 13 and 12 days. The 13-day path can be shortened by up to 2 days at ₹1 lakh/day; the 12-day path by 1 day at ₹2 lakh/day. Normal direct cost is ₹70 lakh and overhead is ₹2.5 lakh per project day. Which feasible schedule has the MINIMUM total cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The normal thirteen-day project costs ₹70 + 13 × ₹2.5 = ₹102.5 lakh. Shortening the longer path by one day costs ₹1 lakh and creates two critical twelve-day paths. At twelve days, total cost is ₹71 + 12 × ₹2.5 = ₹101 lakh. Reaching eleven days requires another ₹1 lakh on the first path and ₹2 lakh on the second path. That produces total cost ₹74 + 11 × ₹2.5 = ₹101.5 lakh. Therefore twelve days has the lowest total cost among the feasible durations.
వివరణ:
Question 18
ప్రశ్న 18
A project has independent A = 6 days and B = 5 days feeding a COMMON final activity C = 4 days. A can be shortened by up to 2 days at ₹2 lakh/day, B by 1 day at ₹3 lakh/day, and C by 1 day at ₹4 lakh/day. C starts only after BOTH A and B finish. Under linear crash costs, what is the MINIMUM incremental DIRECT cost to complete the project in 8 days rather than 10 days?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Normally the project takes max(6, 5) + 4 = 10 days. Shortening A alone by two days still leaves B requiring five days before C, so the project cannot fall below nine days without another action. Reducing A by one day and C by one day changes the two upstream durations to five and five days. The resulting project duration is max(5, 5) + 3 = 8 days. This plan costs ₹2 + ₹4 = ₹6 lakh. The alternative of shortening A twice and B once costs ₹7 lakh, making ₹6 lakh the minimum.
వివరణ:
Question 19
ప్రశ్న 19
Two independent start-to-finish routes originally last 13 and 11 days. Only activity A on the 13-day route can be crashed, by up to 3 days at ₹2 lakh/day; the 11-day route cannot be crashed. What is the MINIMUM additional DIRECT cost required to shorten project completion by exactly 2 days?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The thirteen-day route initially determines project completion. The other route lasts eleven days and cannot be shortened. A two-day reduction of the controlling route makes both paths equal at eleven days. At ₹2 lakh per day, crashing A for two days costs ₹4 lakh. Using the third available crash day would make the first route ten days long but would not shorten the eleven-day project finish. The least expenditure for exactly two days of project acceleration is therefore ₹4 lakh.
వివరణ:
Question 20
ప్రశ్న 20
A network contains two DISJOINT critical start-to-finish paths of 14 days each. All activities on the first path are at their verified crash-duration limits; activities on the second path still have crash capacity. No changes to logic or methods outside those limits are allowed. What is the minimum feasible project duration under the available crashing options?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Project completion requires both independent critical paths to finish. One entire controlling path already takes fourteen days at its minimum feasible activity durations. Crashing the other path cannot reduce the duration of this fixed path. Therefore the project cannot finish before fourteen days under the stated options. The remaining crash capacity on the second path offers no project completion benefit. A shorter deadline would need a justified change to the first path or network assumptions.
వివరణ:
Question 21
ప్రశ్న 21
An activity has a NONLINEAR piecewise crashing schedule: 8 days costs ₹20 lakh; 7 days costs ₹22 lakh; 6 days costs ₹24 lakh; 5 days costs ₹30 lakh. What is the MARGINAL added direct cost of reducing duration from 6 days to 5 days?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The marginal crash cost depends on the two consecutive duration choices being compared. At six days the direct cost is ₹24 lakh. At five days the direct cost is ₹30 lakh. The additional one-day reduction therefore costs ₹30 - ₹24 = ₹6 lakh. Earlier reductions from eight to seven and from seven to six each cost only ₹2 lakh. A single constant cost slope would conceal this more expensive final crash increment.
వివరణ:
Question 22
ప్రశ్న 22
A project has one serial critical path with A = 7 days and B = 5 days. A can be reduced once at ₹1 lakh/day, while B can be reduced by up to two days at ₹4 lakh/day. Normal direct cost is ₹60 lakh and indirect cost is ₹2.5 lakh per project day. What is the optimum project duration and MINIMUM total cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The normal duration is twelve days, yielding total cost ₹60 + 12 × ₹2.5 = ₹90 lakh. Crashing A by one day costs ₹1 lakh and saves ₹2.5 lakh of overhead. At eleven days, total cost is ₹61 + 11 × ₹2.5 = ₹88.5 lakh. Further crashing of B costs ₹4 lakh per day and saves only ₹2.5 lakh per day. At ten days the cost rises to ₹65 + ₹25 = ₹90 lakh, and at nine days it rises again. Hence eleven days gives the minimum total cost.
వివరణ:
Question 23
ప్రశ్న 23
A project has two independent required start-to-finish branches of 16 and 13 days. The only proposed crash is to shorten an activity on the 13-day branch by 2 days at ₹2 lakh/day. Time-related overhead is ₹3 lakh per project day and all other costs remain unchanged. What is the change in TOTAL project cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The sixteen-day branch sets the original project completion. Shortening the other branch from thirteen to eleven days does not change that controlling duration. Consequently the project still lasts sixteen days after the action. The project gains no time-related overhead saving. Direct expenditure nevertheless increases by 2 × ₹2 = ₹4 lakh. Total project cost therefore increases by ₹4 lakh.
వివరణ:
Question 24
ప్రశ్న 24
A project has only THREE feasible evaluated time-cost alternatives, with (duration, direct cost) of (14 days, ₹90 lakh), (13 days, ₹91.5 lakh), and (12 days, ₹94 lakh). Indirect project cost is ₹2 lakh per day. Which alternative has the MINIMUM total project cost?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Total project cost equals the stated direct cost plus time-related indirect cost. At fourteen days it is ₹90 + 14 × ₹2 = ₹118 lakh. At thirteen days it is ₹91.5 + 13 × ₹2 = ₹117.5 lakh. At twelve days it is ₹94 + 12 × ₹2 = ₹118 lakh. The lowest of these evaluated totals is ₹117.5 lakh. Therefore the thirteen-day option is optimum among the three feasible alternatives.
వివరణ:
Question 25
ప్రశ్న 25
A zero-lag CPM network consists of A = 5 days followed by fixed C = 4 days, and B = 4 days followed by fixed D = 5 days; both branches must finish before COMMON E = 3 days. Available reductions are A: 1 day at ₹2 lakh/day; B: up to 2 days at ₹1 lakh/day; E: 1 day at ₹4 lakh/day. What are the MINIMUM feasible project duration and LEAST added direct cost to achieve it?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Both upstream paths initially take nine days and E adds three, so normal project duration is twelve days. A can shorten its path by only one day, leaving a minimum upstream duration of eight days on that branch. E can shorten by only one day, to two days. Thus the minimum feasible project duration is at least 8 + 2 = 10 days. To reach ten days, A must be shortened once, B must be shortened at least once, and E must be shortened once. Their least additional direct cost is ₹2 + ₹1 + ₹4 = ₹7 lakh.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: C. Normal time and cost describe the least-direct-cost operating mode, whereas crash time is the minimum feasible duration with its associated direct cost. సమాధానం: C.
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Question 2 ప్రశ్న 2Answer: B. ₹6 lakh per day. సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: D. ₹33 lakh. సమాధానం: D.
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Question 4 ప్రశ్న 4Answer: A. The proposed 9-day activity duration is infeasible under the given crash-time limit. సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: C. Crash B by one day for ₹2 lakh. సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: B. Completion stays at 15 days, with ₹4 lakh additional direct cost. సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: A. 16 days; ₹4 lakh; both A–C and B–D become critical. సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: D. Crash common activity E by one day for ₹5 lakh. సమాధానం: D.
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Question 9 ప్రశ్న 9Answer: C. ₹5 lakh. సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: B. ₹10 lakh. సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: D. 10 days. సమాధానం: D.
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Question 12 ప్రశ్న 12Answer: A. ₹95 lakh. సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: C. ₹194 lakh, an increase of ₹2 lakh. సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: B. Total project cost decreases by ₹0.5 lakh. సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: D. ₹82 lakh at 15 days. సమాధానం: D.
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Question 16 ప్రశ్న 16Answer: A. ₹138 lakh at 12 days, with no crashing. సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: C. 12 days at ₹101 lakh. సమాధానం: C.
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Question 18 ప్రశ్న 18Answer: B. ₹6 lakh. సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: D. ₹4 lakh, by shortening A two days. సమాధానం: D.
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Question 20 ప్రశ్న 20Answer: C. 14 days, because the uncrashable first critical path still requires 14 days. సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: A. ₹6 lakh for the additional one-day reduction. సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: B. 11 days and ₹88.5 lakh. సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: C. Increase of ₹4 lakh. సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: D. 13 days at ₹117.5 lakh. సమాధానం: D.
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Question 25 ప్రశ్న 25Answer: C. 10 days and ₹7 lakh. సమాధానం: C.