Skip to content

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

The demand for a product of Gupta Industries is p = 90 − 3x, where p is the price in rupees and x is units sold. What price maximises total revenue?

Revenue is 90x minus 3x squared. Setting its derivative 90 minus 6x to zero gives 15 units. Substituting into the demand function gives price 90 minus 45, which equals Rs 45. The second derivative is negative, so revenue is maximised at that price.

  1. ARs 30
  2. BRs 60
  3. CRs 45Correct
  4. DRs 90

Explanation

Revenue R = px = 90x − 3x². dR/dx = 90 − 6x = 0 gives x = 15. Price = 90 − 45 = 45. The second derivative −6 is negative, so it is a maximum. Rs 30 would be the quantity-based mistake of using x = 10, and Rs 60 wrongly uses x = 10 in the price.

Did you get it right without looking?

One question tells you little. A timed set on Calculus - Application in Business shows your real accuracy, how long you take and where you lose marks.

Practise Calculus - Application in BusinessFree diagnostic mock

More Calculus - Application in Business questions