|
Question 442071: Hello! I've a conundrum here!
A company believes that there is a linear relationship between the consumer demand for its product and the price charged. When the price was $3 per unit, the demand was 500 units per week. When the unit price was raised to $4, the weekly demand dropped to 300 units. Define D(p) as the quantity per week demanded by consumers at a unit price of $ p.
a) Find a formula for D(p) in terms of p.
b) Currently, the company can produce 400 units every week. What should the price of the product be if the company wants to sell all 400 units?
THANK YOU!
Answer by rwm(914)   (Show Source):
You can put this solution on YOUR website! Treat this as a linear equation with two points.
y=mx+b
x =3 y=500
(3,500)
x=4 y=300
(4,300)
So we have two points on the line.
and we want the formula (equation)
where we use D(p) for y and p for x
D(p)=mp+b
m=change in y over the change in x
(500-300)/3-4
-200 is m
D(p)=-200p+b
500=-200*3+b
500=-600+b
1100=b
D(p)=-200p+1100
|
|
|
| |
