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

The profit function is given by \(P(x) = R(x) - C(x)\). Simplifying the expression: \[ P(x) = 83x - 4x^2 - 21 - (x^2 - 12x + 48x + 11). \] To find critical points, differentiate \(P(x)\) and set the derivative equal to zero. Solving for \(x\) yields the production level that maximizes profit, which occurs at \(x = 7\).