Question:

For a certain establishment, the total revenue function $R$ and the total cost function $C$ are given by \[ R = 83x - 4x^2 - 21 \quad \text{and} \quad C = x^2 - 12x + 48x + 11, \] where $x$ is the output. Obtain the output for which profit is maximum.

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Understand the levels of management for effective delegation and decision making
Updated On: Jan 8, 2025
  • x = 7
  • x = 9
  • x = 8
  • x = 6
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The Correct Option is A

Solution and Explanation

Profit function $P(x) = R(x) - C(x)$.Simplify: \[ P(x) = 83x - 4x^2 - 21 - (x^2 - 12x + 48x + 11). \] Differentiate $P(x)$ and equate to zero to find critical points. Solve for $x$.Maximum profit occurs at $x = 7$.

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