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The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of Rs. 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
- a)5
- b)10
- c)15
- d)25
Correct answer is option 'A'. Can you explain this answer?
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The cost function for a product in a firm is given by 5q2, where q is ...
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The cost function for a product in a firm is given by 5q2, where q is ...
Given:
Cost function: C(q) = 5q^2
Market price: P = Rs. 50 per unit
To Find:
Number of units to be produced such that the profit is maximized.
Solution:
Profit Function:
Profit is given by the difference between revenue and cost.
Profit = Revenue - Cost
Profit = P*q - C(q)
Profit = 50q - 5q^2
Maximizing Profit:
To find the number of units that maximize the profit, we need to find the maximum of the profit function.
Step 1: Find the derivative of the profit function with respect to q.
Profit'(q) = 50 - 10q
Step 2: Set the derivative equal to zero and solve for q.
50 - 10q = 0
10q = 50
q = 5
Step 3: Check the second derivative to confirm that it is a maximum.
Profit''(q) = -10
Since the second derivative is negative, the profit function has a maximum at q = 5.
Conclusion:
Therefore, the number of units to be produced by the firm such that the profit is maximized is 5 units.
Cost function: C(q) = 5q^2
Market price: P = Rs. 50 per unit
To Find:
Number of units to be produced such that the profit is maximized.
Solution:
Profit Function:
Profit is given by the difference between revenue and cost.
Profit = Revenue - Cost
Profit = P*q - C(q)
Profit = 50q - 5q^2
Maximizing Profit:
To find the number of units that maximize the profit, we need to find the maximum of the profit function.
Step 1: Find the derivative of the profit function with respect to q.
Profit'(q) = 50 - 10q
Step 2: Set the derivative equal to zero and solve for q.
50 - 10q = 0
10q = 50
q = 5
Step 3: Check the second derivative to confirm that it is a maximum.
Profit''(q) = -10
Since the second derivative is negative, the profit function has a maximum at q = 5.
Conclusion:
Therefore, the number of units to be produced by the firm such that the profit is maximized is 5 units.
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The cost function for a product in a firm is given by 5q2, where q is the amount of production. Thefirm can sell the product at a market price of Rs. 50 per unit. The number of units to be produced bythe firm such that the profit is maximized isa)5b)10c)15d)25Correct answer is option 'A'. Can you explain this answer?
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