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.

• A. x = 7
• B. x = 9
• C. x = 8
• D. x = 6

Hint:

Understand the levels of management for effective delegation and decision making

Answer 1

The Correct Option is A

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 $x = 7$.