Question 1167294: The supply and demand for a product are given by
2p − q = 60 and pq = 100 + 25q,
respectively. Find the market equilibrium point.
p,q=
Answer by Resolver123(6)   (Show Source):
You can put this solution on YOUR website! We are given the supply and demand equations:
Supply equation: 2p - q = 60 ...................(1)
Demand equation: pq = 100 + 25q ................(2)
The market equilibrium point occurs where supply = demand, which means we need to find the values of p and q that satisfy both equations simultaneously.
Solve equation (1) for p:
From the supply equation:
2p - q = 60 => 2p = 60 + q =>  ........(3)
Substitute (3) into (2):
 , or 
Rearrange the terms into a quadratic equation
 , or  .
The left side of the quadratic equation can be factored as  , giving q = -20 or q = 10.
Eliminate q = -20 since it is negative. Therefore, q = 10. So the equilibrium quantity is q = 10.
Substitute q = 10 into equation (3) to find the corresponding price:
 . Hence, the equilibrium price is p = 35.
Thus, the market equilibrium point is (q, p) = (10, 35), which means that the market is in equilibrium when 10 units are sold at a price of $35.
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