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

A firm faces demand p = 100 − 2x and total cost C = 20x + 100 (Rs). The government imposes a tax of Rs 8 per unit sold, which adds to cost. What is the maximum profit after the tax?

With the tax, unit cost becomes 28, so profit is 72x minus 2x squared minus 100. Maximising gives 18 units and a profit of Rs 548. This calculation shows the listed key does not match, so the question needs revision.

  1. ARs 700
  2. BRs 828
  3. CRs 668Correct
  4. DRs 800

Explanation

Profit = (100 − 2x)x − (28x + 100) = 72x − 2x² − 100. dπ/dx = 72 − 4x = 0 gives x = 18. π = 72×18 − 2×324 − 100 = 1296 − 648 − 100 = 548. Check: price 64, margin per unit 64 − 28 = 36, 36×18 = 648, minus 100 = 548. So the answer is Rs 548, which is not listed correctly; the nearest key is not valid.

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