Maximizing Revenue Through Optimization

00:00 6 marks

A company models its revenue, \(R(x)\) in thousands of dollars, as a function of the number of units produced, \(x\), with the formula \(R(x) = -2x^2 + 120x\). Determine the number of units that must be produced to maximize the company’s revenue. Calculate and state the maximum revenue in thousands of dollars. Show all steps of your calculus-based optimization process.

Hint Hint

Hint

To maximize revenue, you need to find the vertex of the parabola represented by \(R(x)\) using calculus. This involves finding the derivative of \(R(x)\) and setting it equal to zero to locate the critical point.

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Complete Answer

The revenue is maximized when \(x = 30\) units, and the maximum revenue is \(1800\) thousand dollars.

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