Question

3. Suppose that the demand function for a certain brand of shampoo is D(x) = –1.25x + 525. What is the highest price anyone will be willing to pay for the shampoo?

Please include the complete solution.

Answer 1

ANS: Maximum Price = $ 420. per unit

As given, demand function is D(x) = -1.25x + 525.

As we all know, the company will be ready to set any price as far as there is demand for the product in the market. Alternatively we can say that, as long as the demand function stays positive, so far the price could be changed. But once the demand reach NIL, the company cannot increase the price.

Hence, to find the maximum price that could be charged, we have to find that value of "x" where Demand function =0.

ie,

0 = -1.25x + 525

1.25x = 525

x = 525/1.25 = 420

When Price per unit = $ 420, demand function will be:

D (x=420) = -1.25 ( 420 ) + 525 = -525 + 525 = 0.