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The weekly demand and supply functions for Sportsman 5 × 7 tents are given by
p = −0.1x^2 − x + 33
p = 0.1x^2 + 2x + 13
respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity. Find the equilibrium price.

Answer :

nobillionaireNobley
The equilibruim point of a demand and supply function is the point at which the quantity demanded is equal to the quantity supplied.

Given the demand function as
[tex]p = -0.1x^2 - x + 33[/tex]
and the supply function as
[tex]p = 0.1x^2 + 2x + 13[/tex]

The equilibruim quantity is obtained as follows:
[tex]-0.1x^2 - x + 33=0.1x^2 + 2x + 13 \\ \\ \Rightarrow0.2x^2+3x+46=0 \\ \\ \Rightarrow x=-7.5\pm13.18i[/tex]

There is no real equilibruim quantity and price for the given demand and supply function.

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