Question

A large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $4 each, but only 3,500 shower curtains per month for $9 each. what is the linear demand function for your tie-dye shower curtains?

Answer 1

D(p) = 4040 - 60p 
where 
p = price.  
We want to create a function D() such that D(4) = 3800 and D(9) = 3500. The basic formula will be that of a line in slope intercept form. Picking a line since we've only been given 2 data points and 2 points define a line and because we've been asked for a "linear demand function". The basic form for a line in slope intercept form is: 
y = ax + b
 where 
a = slope
b = y intercept  
Let's calculate the slope which is the difference in y divided by the difference in x, so 
(3500 - 3800)/(9-4) = -300/5 = -60  
So the equation so far is: 
y = -60x + b  
Now to calculate b. To do so, just substitute a known x and y pair. So 
y = -60x + b 
3800 = -60*4 + b 
3800 = -240 + b 
4040 = b  
And we have the equation: 
y = -60x + 4040  
So the demand function is 
D(p) = 4040 - 60p 
where 
p = price.