Question 1167294
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 => {{{p = (60 + q)/2}}}........(3)


Substitute (3) into (2):

{{{((60+q)/2)*q = 100 + 25q}}}, or {{{(60+q)*q=2*(100+25q)}}}


Rearrange the terms into a quadratic equation

{{{60q + q^2 = 200 + 50q}}}, or {{{q^2 + 10q - 200 = 0}}}.


The left side of the quadratic equation can be factored as {{{(q+20)(q-10) = 0}}}, 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:

{{{p = (60 + 10)/2 = 70/2 = 35}}}. 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.