Question

large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $5 each, but only 3,500 per month for $10 each. What is the linear demand function for your tie-dye shower curtains?

Answer 1

Answer:

$D(p)=-60p+4100$.

Step-by-step explanation:

We have been given that a large department store is prepared to buy 3,800 of your tie-dye shower curtains per month for $5 each, but only 3,500 per month for $10 each.  

We have been given two points on a line (5,3800) and (10,3500).

Let us find slope of the line using slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{3500-3800}{10-5}$

$m=\frac{-300}{5}$

$m=-60$

Now, we will use point-slope form to write our required equation.

$y-y_1=m(x-x_1)$

$y-3500=-60(x-10)$

$y-3500=-60x+600$

$y-3500+3500=-60x+600+3500$

$y=-60x+4100$

Therefore, our demand function would be $D(p)=-60p+4100$, where p represents price.