Question

18) A company is planning to manufacture a new blender. After conducting extensive

market surveys, the research department estimates a weekly demand of 600 blenders at
a price of $50 per blender and a weekly demand of 800 blenders at a price of $40 per
blender. Assuming the demand equation is linear, use the research department's
estimates to find the revenue equation in terms of the demand x.

Answer 1

R(x) = -0.05x^2 +80x

Explanation:

Given the two points (x, p), the equation for the price associated with a given demand quantity can be written using the 2-point form:

p = (p2 -p1)/(x2 -x1)(x -x1) +p1

p = (40 -50)/(800 -600)(x -600) +50

p = -0.05x +80 . . . . simplify

Then the revenue equation is ...

R(x) = xp

R(x) = -0.05x^2 +80x