GATE Exam > GATE Questions > The cost function for a product in a firm is ...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The cost function for a product in a firm is given by 5q2, where q is ...
Most Upvoted Answer
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.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
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?
Question Description
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? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup