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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business

A Jaipur firm has total cost C(x) = x² + 20x + 900 and sells each unit at a fixed price of ₹80. What is the break-even output (positive, non-zero)?

At break-even, revenue equals cost: 80x = x² + 20x + 900. This simplifies to x² − 60x + 900 = 0, a perfect square giving x = 30 units. At 30 units both revenue and cost equal ₹2,400.

  1. A30 unitsCorrect
  2. B20 units
  3. C45 units
  4. D15 units

Explanation

Break-even when R = C: 80x = x² + 20x + 900, so x² − 60x + 900 = 0, i.e. (x − 30)² = 0, x = 30. Check: R = 2,400; C = 900 + 600 + 900 = 2,400. Other options give unequal revenue and cost.

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