CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
The demand function is p = 60 − 3x, where p is the price in ₹ and x is the quantity. What is the maximum total revenue the firm can earn?
The maximum total revenue is ₹300. Revenue is 60x − 3x², and setting its derivative 60 − 6x to zero gives x = 10. The second derivative is negative, so it is a maximum, and the revenue is 600 − 300 = ₹300.
- A₹300Correct
- B₹600
- C₹150
- D₹200
Explanation
R = px = 60x − 3x². dR/dx = 60 − 6x = 0 gives x = 10, and the second derivative −6 is negative. R = 600 − 300 = ₹300. ₹600 is 60x at x = 10, which forgets to subtract 3x².
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