Comprehension
Answer the questions based on the following information. Ghosh Babu has a manufacturing unit.
The following graph gives the cost for various number of units. Given: Profit = Revenue – Variable cost – Fixed cost. The fixed cost remains constant up to 34 units after which additional investment is to be done in fixed assets. In any case, production cannot exceed 50 units.
Question: 1
What is the minimum number of units that need to be produced to make sure that there was no loss?
What is the minimum number of units that need to be produced to make sure that there was no loss?
Show Hint
To avoid loss, ensure total revenue equals or exceeds total cost. Match cost and revenue values from graph for smallest such point.
Updated On: Aug 4, 2025
- 5
- 10
- 20
- Indeterminable
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The Correct Option is B
Solution and Explanation
From the graph, we observe the following:
- Fixed cost = Rs. 200 (constant up to 34 units)
- Revenue and Variable cost increase linearly with production. To ensure no loss: \[ \text{Profit} = \text{Revenue} - \text{Variable Cost} - \text{Fixed Cost} \geq 0 \] Let’s test where the Revenue line meets or surpasses the total cost line: Total cost = Variable cost + Fixed cost
At 10 units: - Revenue ≈ Rs. 400
- Variable cost ≈ Rs. 200
- Fixed cost = Rs. 200
- Total cost = Rs. 200 + Rs. 200 = Rs. 400
\[ \text{Profit} = 400 - 400 = 0 \] Hence, at 10 units there is no loss. \[ \boxed{\text{Minimum units to avoid loss} = 10} \]
- Revenue and Variable cost increase linearly with production. To ensure no loss: \[ \text{Profit} = \text{Revenue} - \text{Variable Cost} - \text{Fixed Cost} \geq 0 \] Let’s test where the Revenue line meets or surpasses the total cost line: Total cost = Variable cost + Fixed cost
At 10 units: - Revenue ≈ Rs. 400
- Variable cost ≈ Rs. 200
- Fixed cost = Rs. 200
- Total cost = Rs. 200 + Rs. 200 = Rs. 400
\[ \text{Profit} = 400 - 400 = 0 \] Hence, at 10 units there is no loss. \[ \boxed{\text{Minimum units to avoid loss} = 10} \]
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Question: 2
How many units should be manufactured such that the profit was at least Rs. 50?
How many units should be manufactured such that the profit was at least Rs. 50?
Show Hint
Use the graph to estimate Revenue and Cost at various points. Subtract to find profit and match conditions.
Updated On: Aug 4, 2025
- 20
- 34
- 45
- 30
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The Correct Option is A
Solution and Explanation
We are given:
\[
\text{Profit} = \text{Revenue} - \text{Variable Cost} - \text{Fixed Cost}
\]
We need profit \(\geq 50\). From the graph:
- At 20 units, revenue ≈ Rs. 600
- Variable cost ≈ Rs. 350
- Fixed cost = Rs. 200
- Profit = 600 - 350 - 200 = Rs. 50
\[ \boxed{\text{Minimum units to get profit of at least 50 is } 20} \]
- Variable cost ≈ Rs. 350
- Fixed cost = Rs. 200
- Profit = 600 - 350 - 200 = Rs. 50
\[ \boxed{\text{Minimum units to get profit of at least 50 is } 20} \]
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Question: 3
If at the most 40 units can be manufactured, then what is the number of units that can be manufactured to maximise profit per unit?
If at the most 40 units can be manufactured, then what is the number of units that can be manufactured to maximise profit per unit?
Show Hint
When fixed cost increases beyond a point, profit per unit often dips. Maximize before cost jump.
Updated On: Aug 4, 2025
- 40
- 34
- 35
- 25
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The Correct Option is B
Solution and Explanation
We are to find maximum profit per unit under the constraint of max 40 units.
Let us define:
\[
\text{Profit per unit} = \frac{\text{Total Profit}}{\text{Units Produced}}
\]
We observe from the graph:
- Fixed cost remains constant up to 34 units.
- Beyond 34, fixed cost increases sharply, hence reducing per-unit profit.
- Hence, maximum profit per unit occurs at 34 units before fixed cost rises.
\[
\boxed{\text{Optimal production for max profit per unit} = 34}
\]
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Question: 4
If the production cannot exceed 45 units, then what is the number of units that can maximise profit per unit?
If the production cannot exceed 45 units, then what is the number of units that can maximise profit per unit?
Show Hint
More production does not always mean higher per-unit profit. Watch for sudden cost jumps.
Updated On: Aug 4, 2025
- 40
- 34
- 45
- 35
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The Correct Option is B
Solution and Explanation
Although 45 units is allowed, the fixed cost increases after 34 units.
This reduces profit per unit for higher production.
So, maximum profit per unit occurs at the edge before fixed cost rises. That is 34.
\[
\boxed{\text{Best output for max profit per unit under 45-unit cap} = 34}
\]
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Question: 5
If the fixed cost of production goes up by Rs. 40, then what is the minimum number of units that need to be manufactured to make sure that there is no loss?
If the fixed cost of production goes up by Rs. 40, then what is the minimum number of units that need to be manufactured to make sure that there is no loss?
Show Hint
If fixed cost rises, break-even production also increases. Match new cost with revenue.
Updated On: Aug 4, 2025
- 10
- 19
- 15
- 20
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The Correct Option is B
Solution and Explanation
Earlier, no loss occurred at 10 units with fixed cost Rs. 200.
Now fixed cost = Rs. 240.
We find the minimum number of units such that:
\[
\text{Revenue} = \text{Variable Cost} + 240
\]
By checking graph estimates, this balance occurs approximately at 19 units:
- Revenue ≈ Rs. 570
- Variable cost ≈ Rs. 330
- Total cost = 330 + 240 = Rs. 570 \[ \boxed{\text{Minimum units for no loss with higher fixed cost} = 19} \]
- Variable cost ≈ Rs. 330
- Total cost = 330 + 240 = Rs. 570 \[ \boxed{\text{Minimum units for no loss with higher fixed cost} = 19} \]
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