CUET · MATHS · PYQ PAPER 2025
The marginal cost (MC) and marginal revenue (MR) functions of a product are \(M C=20+\frac{x}{20}\) and \(M R=30\) respectively. If the fixed cost is 200 , then the maximum value of the profit is :
- A Rs. 750
- B Rs. 800
- C Rs. 640
- D Rs. 940
Answer & Solution
Correct Answer
(B) Rs. 800
Step-by-step Solution
Detailed explanation
\(MC = MR\) \(20 + \frac{x}{20} = 30\) \(\frac{x}{20} = 10\) \(x = 200\) \(C(x) = \int MC \, dx + FC = \int (20 + \frac{x}{20}) \, dx + 200\) \(C(x) = 20x + \frac{x^2}{40} + 200\) \(R(x) = \int MR \, dx = \int 30 \, dx\) \(R(x) = 30x\) \(P(x) = R(x) - C(x)\)…
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