A firm's profit function is P(q) = -q² + 40q - 100, where q is the number of units produced. At what output is profit maximised?
Correct answer: B. 20 units
- A. 10 units
- B. 20 units
- C. 30 units
- D. 40 units
Explanation
The derivative is P'(q) = -2q + 40. Setting marginal profit equal to zero gives q = 20, and the negative coefficient of q² confirms that this is a maximum.
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About Differentiation and Optimisation
Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
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