CMA Final · Strategic Cost Management · Business Application of Maxima and Minima
A firm's total cost function is C(x) = 2x^2 - 40x + 500, where x is units produced per day. At what output is total cost minimised?
Cost is minimised at 10 units. The first derivative, 4x - 40, equals zero at x = 10, and the second derivative is positive (4), confirming a minimum rather than a maximum.
- A5 units
- B10 unitsCorrect
- C20 units
- D40 units
Explanation
Differentiate: C'(x) = 4x - 40. Setting this to zero gives x = 10. C''(x) = 4 > 0, so this is a minimum. The value 20 comes from solving 2x - 40 = 0, which ignores the coefficient 2 on x squared.
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