The manufacturing company produces \(x\) items at the total cost of ₹ (180+4\(x\)). The demand function for this product is \(P=(240-x)\). Find \(x\) for which profit is increasing.

Q.3 (A) (iii) The manufacturing company produces \(x\) items at the total cost of ₹ (180+4\(x\)). The demand function for this product is \(P=(240-x)\). Find \(x\) for which profit is increasing.

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

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Answer: Profit is increasing for \(x\lt 118\).

Revenue \(R=P\cdot x=(240-x)x=240x-x^2\). Cost \(C=180+4x\).

Profit \(\pi=R-C=240x-x^2-180-4x=236x-x^2-180\).

\(\frac{d\pi}{dx}=236-2x\). Profit is increasing when \(\frac{d\pi}{dx}\gt 0\): \(236-2x\gt 0\Rightarrow x\lt 118\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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The manufacturing company produces \(x\) items at the total cost of ₹ (180+4\(x\)). The demand function for this product is \(P=(240-x)\). Find \(x\) for which profit is increasing.

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