Question 33505
Hello!
This question can be easily solved in the following way.

We call "equilibrium price" to the the price (the value of "p") that makes demand equal supply. So we simply have to set up the equation:

D = S

Since:

{{{D= -200p + 35000}}}
{{{S= -p^2 + 400p - 20000}}}

Then, from D = S, we get:

{{{-200p + 35000 = -p^2 + 400p - 20000}}}

After combining like terms, we're left with:

{{{-p^2 + 600p - 55000 = 0}}}

This quadratic equation can then be solved using the quadratic formula:

*[invoke solve_quadratic_equation -1, 600, -55000]


So there are two solutions: p=112.91 or p=487.08. However, notice that the 487.08 solution doesn't make sense, as supply and demand are negative in this case (try plugging p=487.08 into either the supply or demand formula). Therefore, the correct answer is that the equilibrium price is 112.91.


I hope this helps!
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