An important application of systems of equations arises in c

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

a) How many hand-held color televisions can be sold at $ 360 per television?
Answer:

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

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

Solution

a) At the price of 360$, supply model will have number of televisions equal to

Supply Model: 3.3p = 3.3*360 = 1188 units

Demand Model = -4p + 3199 = 1759 units

Since the demand of TV is more as compared to the supply from the company hence all the TV\'s can be send for sale

Hence correct answer is 1188 units

b) Number of television sold when demand and supply are equal

-4p + 3139 = 3.3p

7.3p = 3139

p = 430 units

Hence the number of television sold will be equal to 430 when the demand and supply curve are equal

c) The price of television can be found by substituting the value of p=430 in any of demand/supply equation

N = -4p + 3139

=> -4(430) + 3139

=> -1720 + 3139

=> 1419$

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