CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A Surat firm has demand p = 120 - 0.5x, where p is price in rupees and x is units sold. What is the output that maximises total revenue?
Revenue is maximised at 120 units. Revenue equals 120x minus 0.5x squared, its derivative is 120 minus x, and setting this to zero gives x = 120.
- A60
- B120
- C240Correct
- D180
Explanation
Revenue R = px = 120x - 0.5x^2. R' = 120 - x = 0 gives x = 120... check: derivative of 0.5x^2 is x, so x = 120. Hence the correct value is 120, and 240 is wrong because it sets p = 0 (the x-intercept) instead of MR = 0.
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