Question

Based upon market research, the Hawthone Company has determined that consumers are willing to purchase 121 units of their portable media player each week when the price is set at s96.90 per unit. At a unit price f 40.20,cosumers are wiling to buy 310 units per week (a) Determine the weekdy denund equation for this product, ansuming price, p, and quantity, x, are inearly related b) Determine the weekdy revenue fanction A(x) of wnits consumers will demand weekly when the price is $50.70 per portable media player d Determine the mumber of ts consumers will demand weekly when the revenue is maximieed )Detormine the price of each unit when the revene is maximized

Answer 1

Answer:

Step-by-step explanation:

Given that price, p, and quantity, x, are inearly related

We are given two points on this line as (p,x) = (96.90, 121) and (40.20,310)

Using two point formula we find linear equation as

$\frac{y-121}{310-121} =\frac{0-96.90}{40.20-96.90} \\(x-121)(-56.70)=189(p-96,.90)\\189p+56.70x =25174.80$

a)$189p+56.70x =25174.80$ is the linear equation

b) A(x)

Substitute to get

189(50.70)+56.70x = 25174.80

x=275 units

c) This is linear function hence no local maxima or minima

d) No maximia or minima