help with calculus

Question

An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that produce decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. Suppose a chain of electronics stores sells hand-held color televisions. The weekly demand and supply models are given as follows:

Demand model: N=-4p+3168

Supply model: N=2.6p

b) How many televisions will be sold when supply and demand are equal?

c) Find the price at which supply and demand are equal.

Answer 1

Hi Mylene,

So it will be easier to start with part C. The question is asking us to find the point at which the demand equation will be equal to the supply equation.

Since we know,

Demand model: N = -4p + 3168

Supply model: N = 2.6p

We are looking for the value of p that would make the demand model equal to the supply model. This can be written as,

-4p + 3168 = 2.6p

Now we just have to solve for p using some algebra,

First, we add 4p to both sides of the equation to get all the p's on one side.

-4p + 4p + 3168 = 2.6p + 4p

3168 = 6.6p

Then we can divide both sides by 6.6 to solve for p

3168 / 6.6 = 6.6p / 6.6

480 = p

This means that when the price is 480, the supply will equal the demand.

To find the number of TVs that will be sold, we solve for N by substituting 480 for p in either equation.

N = 2.6p

N = 2.6(480)

N = 1248

This means that when the supply and demand are equal, the number of TVs sold will be 1248.

I hope that helped!