CMA Final · Strategic Cost Management · Business Application of Maxima and Minima
A firm's total cost function is C(x) = 2x^2 - 40x + 500 (in rupees thousand), where x is units produced in hundreds. At what output x is total cost minimum?
Output of 10 (hundred units) minimises total cost. Setting the first derivative 4x - 40 to zero gives x = 10, and the positive second derivative of 4 confirms a minimum rather than a maximum.
- A5
- B10Correct
- C20
- D40
Explanation
dC/dx = 4x - 40 = 0 gives x = 10. The second derivative is 4, which is positive, so this is a minimum. Choosing 20 comes from wrongly solving 2x - 40 = 0 (differentiating the x^2 term without the multiplier of 2).
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