CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A firm's profit function is P(x) = 120x - 3x^2 (in rupees thousand), where x is the number of units produced in hundreds. At what value of x is profit maximised?
Profit is maximised at x = 20. Setting the first derivative 120 - 6x equal to zero gives x = 20, and the second derivative is -6, which is negative, confirming a maximum rather than a minimum.
- A10
- B20Correct
- C30
- D40
Explanation
P'(x) = 120 - 6x = 0 gives x = 20. P''(x) = -6 < 0, so this is a maximum. Choosing x = 40 comes from setting 120 - 3x = 0, which uses the wrong derivative of the quadratic term.
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