CMA Final · Strategic Cost Management · Business Application of Maxima and Minima
A manufacturer sells x units at a price p = 120 - 0.5x rupees per unit. Variable cost is Rs 40 per unit, and fixed cost is Rs 2,000. What output maximises profit?
Profit is maximised at 80 units. Marginal revenue is 120 minus x and marginal cost is Rs 40, so equating them gives x equal to 80. The second derivative of profit is negative, confirming a maximum.
- A60 units
- B80 unitsCorrect
- C100 units
- D120 units
Explanation
Revenue = 120x - 0.5x², so MR = 120 - x. MC = 40. Setting MR = MC gives x = 80. The second derivative of profit is -1, which is negative, so it is a maximum. Choosing 160 would come from setting price equal to MC, ignoring that MR falls twice as fast as price (here 60 is not obtained either).
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