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 electronies stores sells hand-held color televisions. The weeklydemand and supply models are given as followsDemand model: N = 6p -6p+4356Supply Model: N = 3.9pDemand model:N = -6p + 4356Supply model:N = 3.9pwhere N is the number of televisions sold each week and at price p. Answer with the appropriate units.a) How many hand-held color televisions can be sold at $ 500 per television?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

From the problem, we have the demand and supply model.

Demand :

`N=-6p+4356`

Supply :

`N=3.9p`

a. The number of demand that can be sold at p = $500 is :

`\begin{gathered} N=-6(500)+4356 \\ N=1356 \end{gathered}`

The answer is 1356

c. The price which supply and demand are equal. Equate demand and supply :

`\begin{gathered} \text{Demand}=\text{Supply} \\ -6p+4356=3.9p \\ -6p-3.9p=-4356 \\ -9.9p=-4356 \\ p=(-4356)/(-9.9)=440 \end{gathered}`

The answer is $440

b. The number of television when p = 440

`\begin{gathered} N=-6p+4356 \\ N=-6(440)+4356 \\ N=1716 \end{gathered}`

The answer is 1716

To summarized, the answers are :

a. 1356

b. 1716

c = $440