The equilibrium quantity obtained from the equilibrium supply and demand functions is 500 units
The steps by which the equilibrium quantity is obtained can be presented as follows;
The demand and supply functions are presented as follows;
p = -0.1·x² - x + 76
p = 0.1·x² + 2·x + 56
The equilibrium quantity is the quantity at which the demand and supply functions for the price are equivalent. Therefore, at the equilibrium quantity, we get;
-0.1·x² - x + 76 = 0.1·x² + 2·x + 56
0.2·x² + 3·x - 20 = 0;
The division of both sides of the above equation by 0.2 indicates that we get;
(0.2·x² + 3·x - 20)/0.2 = 0/0.2
x² + 15·x - 100 = 0
(x + 20)·(x - 5) = 0
x = -20, and x = 5
Therefore, the equilibrium quantity is 500 units
The possible complete question found through search can be presented as follows;
Market Equilibrium; The weekly demand and supply functions for Sportsman 5 × 7 tents are expressed using the functions in the question;
p = -0.1·x² - x + 76
p = 0.1·x² + 2·x + 56
Respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity (in hundred units)