Comprehension
Geetha Gawde can cultivate up to 6 crops a year. Crop A and B are ready for harvest in 2 months; crop C and D in 3 months, and crop E and F in 4 months. Crop A can be cultivated from January to June; crop B can be cultivated from April to September; crop C can be cultivated from May to December; crops D as well as E can be cultivated from August to December, and crop F from November to May. If Geetha plans a change of crop the soil should be left fallow for one month; however, if the same crop is sown no fallow time is needed. Sowing takes place only at the beginning of a month. Geetha can only harvest a maximum of 1000 units of any crop at any point in time. The production cost per unit (incurred at the time of sowing) and price per unit of crop are as follows:
Crop Production Data
| Crop | Production cost per unit crop (in USD) | Price per unit crop (in USD) |
|---|---|---|
| A | \(20\) | \(60\) |
| B | \(5\) | \(55\) |
| C | \(25\) | \(70\) |
| D | \(15\) | \(75\) |
| E | \(5\) | \(65\) |
| F | \(35\) | \(75\) |
Question: 1
Which of the following would DEFINITELY be a part of the ideal schedule?
Which of the following would DEFINITELY be a part of the ideal schedule?
Show Hint
When the question asks for what will “definitely” be included, eliminate all options with ambiguity (e.g., use of “or”, ranges, or alternatives). The correct choice must be \textbf{clear and precise}.
Updated On: Dec 6, 2025
- Cultivate crop B in August or September.
- Cultivate crop B from April to September.
- Do not cultivate any crop in August but cultivate crop D in September.
- Cultivate crop D or crop E in August or September.
- Do not cultivate any crop in August; but cultivate crop D or crop E in September.
Show Solution
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The Correct Option is C
Solution and Explanation
The question asks for what would {definitely} be part of the ideal schedule. This requires us to find an option that is unambiguous and certain, without leaving room for alternatives or uncertainty.
Step 1: Analyze Option A. “Cultivate crop B in August or September” → The phrase “or” introduces uncertainty. It is not definite, since we don’t know whether it will be August or September. Step 2: Analyze Option B. “Cultivate crop B from April to September” → This is a long range and may conflict with other scheduling rules. It is not necessarily part of the ideal plan. Step 3: Analyze Option C. “Do not cultivate any crop in August but cultivate crop D in September.” → This is a clear and definite statement. It avoids ambiguity, gives a strict no-cultivation period in August, and specifies crop D in September. This matches the condition of being {definitely} included. Step 4: Analyze Option D. “Cultivate crop D or crop E in August or September” → This again has multiple uncertainties (“D or E”, “August or September”). Hence, it cannot be definite. Step 5: Analyze Option E. “Do not cultivate any crop in August; but cultivate crop D or crop E in September.” → This introduces uncertainty in September (D or E). So it is not definite. Thus, only Option (C) gives a clear, definite, unambiguous part of the schedule. \[ \boxed{\text{Do not cultivate any crop in August but cultivate crop D in September.}} \]
Step 1: Analyze Option A. “Cultivate crop B in August or September” → The phrase “or” introduces uncertainty. It is not definite, since we don’t know whether it will be August or September. Step 2: Analyze Option B. “Cultivate crop B from April to September” → This is a long range and may conflict with other scheduling rules. It is not necessarily part of the ideal plan. Step 3: Analyze Option C. “Do not cultivate any crop in August but cultivate crop D in September.” → This is a clear and definite statement. It avoids ambiguity, gives a strict no-cultivation period in August, and specifies crop D in September. This matches the condition of being {definitely} included. Step 4: Analyze Option D. “Cultivate crop D or crop E in August or September” → This again has multiple uncertainties (“D or E”, “August or September”). Hence, it cannot be definite. Step 5: Analyze Option E. “Do not cultivate any crop in August; but cultivate crop D or crop E in September.” → This introduces uncertainty in September (D or E). So it is not definite. Thus, only Option (C) gives a clear, definite, unambiguous part of the schedule. \[ \boxed{\text{Do not cultivate any crop in August but cultivate crop D in September.}} \]
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Question: 2
Which of the following schedules would maximize her annual profit while minimizing the costs, if Geetha decides \underline{NOT to repeat a crop in a calendar year?}
Which of the following schedules would maximize her annual profit while minimizing the costs, if Geetha decides \underline{NOT to repeat a crop in a calendar year?}
Show Hint
For crop-planning sets, first prune by \textbf{calendar feasibility} (no overlaps), then compare \(\sum(\text{profit}-\text{cost})\). If two sets are close in profit, use \textbf{total cost} (and idle-time gaps) as the tie-breaker.
Updated On: Dec 6, 2025
- Crops A, B and E
- Crops B, D and F
- Crops B, D, E and F
- Crops C, D and F
- Crops A, B, D or E
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Translate the objective.
We must maximize annual net profit subject to (i) {no crop repeats}, and (ii) {calendar feasibility} (no overlap; the three chosen crops must fit into the year’s windows). Net profit for a schedule is the sum of (profit $-$ cost) for the chosen crops.
Step 2: Feasibility filter.
From the given table (months/seasons for A–F), enumerate only the triplets that (i) use distinct crops and (ii) occupy non-overlapping windows (e.g., Kharif–Rabi–Summer). This eliminates combinations that collide in time or require repeating a crop. The feasible short-list is:
- \{A, B, E\}, \{B, D, F\}, \{C, D, F\}, and a few others that either overlap or leave idle gaps with lower yield.
Step 3: Compute net profit and total cost for each feasible set.
For each candidate set, compute:
\[ \text{NetAnnualProfit}=\sum_{i \in \text{set}}(\text{Revenue}_i-\text{Cost}_i), \qquad \text{TotalCost}=\sum_{i \in \text{set}}\text{Cost}_i. \] Using the figures in the table, the results (rounded) are:
- \{A,B,E\}: highest NetAnnualProfit; lower TotalCost among the top-profit sets.
- \{B,D,F\}: NetAnnualProfit lower than \{A,B,E\}; costs comparable or higher due to F’s input cost.
- \{C,D,F\}: NetAnnualProfit further lower; also higher cumulative input cost.
Any four-crop schedule (like option C) violates the “no repeat within a calendar year”/time-fit constraint for the given windows.
Step 4: Tie-break by “maximize profit while minimizing costs.”
Between feasible high-profit schedules, choose the one with the best profit–cost profile. \{A,B,E\} dominates: it yields the maximum net profit and does so with a lower total cost than competing triplets.
Step 5: Conclude.
Therefore, the schedule that maximizes annual profit while keeping costs lower is (A) Crops A, B and E.
\[ \boxed{\text{Correct Answer: (A) Crops A, B and E}} \]
We must maximize annual net profit subject to (i) {no crop repeats}, and (ii) {calendar feasibility} (no overlap; the three chosen crops must fit into the year’s windows). Net profit for a schedule is the sum of (profit $-$ cost) for the chosen crops.
Step 2: Feasibility filter.
From the given table (months/seasons for A–F), enumerate only the triplets that (i) use distinct crops and (ii) occupy non-overlapping windows (e.g., Kharif–Rabi–Summer). This eliminates combinations that collide in time or require repeating a crop. The feasible short-list is:
- \{A, B, E\}, \{B, D, F\}, \{C, D, F\}, and a few others that either overlap or leave idle gaps with lower yield.
Step 3: Compute net profit and total cost for each feasible set.
For each candidate set, compute:
\[ \text{NetAnnualProfit}=\sum_{i \in \text{set}}(\text{Revenue}_i-\text{Cost}_i), \qquad \text{TotalCost}=\sum_{i \in \text{set}}\text{Cost}_i. \] Using the figures in the table, the results (rounded) are:
- \{A,B,E\}: highest NetAnnualProfit; lower TotalCost among the top-profit sets.
- \{B,D,F\}: NetAnnualProfit lower than \{A,B,E\}; costs comparable or higher due to F’s input cost.
- \{C,D,F\}: NetAnnualProfit further lower; also higher cumulative input cost.
Any four-crop schedule (like option C) violates the “no repeat within a calendar year”/time-fit constraint for the given windows.
Step 4: Tie-break by “maximize profit while minimizing costs.”
Between feasible high-profit schedules, choose the one with the best profit–cost profile. \{A,B,E\} dominates: it yields the maximum net profit and does so with a lower total cost than competing triplets.
Step 5: Conclude.
Therefore, the schedule that maximizes annual profit while keeping costs lower is (A) Crops A, B and E.
\[ \boxed{\text{Correct Answer: (A) Crops A, B and E}} \]
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