CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
The total cost of producing x units at a Pune workshop is C(x) = x^2 - 12x + 50 (in rupees hundreds). At what output level is the total cost minimum?
Cost is minimum at 6 units. Setting the first derivative 2x - 12 equal to zero gives x = 6, and the second derivative is positive (2), which confirms that the stationary point is a minimum rather than a maximum.
- Ax = 3
- Bx = 6Correct
- Cx = 12
- Dx = 24
Explanation
C'(x) = 2x - 12 = 0 gives x = 6. C''(x) = 2 > 0, so this is a minimum. Choosing x = 12 comes from forgetting to divide by 2 (taking the coefficient only).
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