Question

A company makes greeting cards and their research shows that that price and demand are related linearly: p = mx + b. They know that for every additional card they wish to sell they need to drop the price by $0.05. They also know that in order to sell 360 cards they need to set the price at $4. Find the linear equation relating price to demand. p= 0 Preview

Answer 1

p = -0.05x+22

Explanation:

The general linear equation of price-demand is

(1) p = mx + b

where x is the demand of cards in units when they are sold at x dollars.

If for every additional card they wish to sell they need to drop the price by $0.05, then

(2) p-0.05 = m(x+1)+b

To sell 360 cards they need to set the price at $4, so

(3) 4 = m.360+b

We need to find m and b.

Operating on eq. (2) we have

p-0.05 = mx+m+b

mx+b-0.05 = mx+m+b

m = -0.05

Replacing this value in (3)

4 = (-0.05)360 +b

4 = -18+b

b = 22

So, the linear equation relating price p to demand x is

p = -0.05x+22

See graph attached.