CMA Final · Strategic Cost Management · Business Application of Maxima and Minima
Demand for a product is p = 200 - 2x (rupees per unit) and total cost is C(x) = 20x + 400. At what output does profit reach its maximum, and what is that maximum profit?
Set marginal revenue equal to marginal cost: 200 - 4x = 20, so output is 45 units. Profit is revenue 8,100 less 4,050 variable-type terms adjustments, giving 8,100 - 4,050 - 400 = Rs 3,650, a maximum since the second derivative is negative.
- Ax = 45 units, profit Rs 7,850
- Bx = 50 units, profit Rs 3,600
- Cx = 45 units, profit Rs 3,650Correct
- Dx = 40 units, profit Rs 3,600
Explanation
Revenue = 200x - 2x^2; profit = 180x - 2x^2 - 400. d/dx = 180 - 4x = 0 gives x = 45. Profit = 180(45) - 2(2025) - 400 = 8,100 - 4,050 - 400 = 3,650. Second derivative -4 confirms a maximum. Option with 7,850 misses deducting properly, and 50 units is wrong marginal condition.
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