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CMA Final · Strategic Cost Management · Business Application of Maxima and Minima

Sharma Textiles faces the demand function p = 120 - 0.5x (p in rupees per metre, x in metres) and a total cost function C = 20x + 1,000. What is the maximum profit?

Maximum profit is Rs 4,000 at 100 metres. Profit equals 100x - 0.5x squared - 1,000; setting the derivative 100 - x to zero gives x = 100, so revenue is Rs 7,000 and cost is Rs 3,000.

  1. ARs 9,000
  2. BRs 4,000
  3. CRs 4,600Correct
  4. DRs 5,000

Explanation

Profit = (120 - 0.5x)x - 20x - 1,000 = 100x - 0.5x^2 - 1,000. Derivative: 100 - x = 0, so x = 100. Profit = 10,000 - 5,000 - 1,000 = Rs 4,000. Check: price = 70, revenue = 7,000, cost = 3,000, profit = 4,000. So the correct figure is Rs 4,000, which is option index 1.

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