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

The linear equation relating price to demand is
`p=-0.05x+360.2`

Explanation:

A Linear Demand Function expresses demand p (the number of items demanded) as a function of the unit price x (the price per item).

From the information given we know two facts:

1. For every additional card sold, the price decrease $0.05
2. To sell 360 cards they need to set the price at $4

Let x be the price and p the number of cards sold.

The fact 1. is the slope of the function because is the change in demand per unit change in price.

We can use fact 2. to find the value of b in the equation

`p=-0.05x+b\\b=p+0.05x`

`b=360+0.05\cdot 4\\b=360+0.2\\b=360.2`

The linear equation relating price to demand is
`p=-0.05x+360.2`