Soru
For a supply equation p=sqrt (q+10) and demand equation p=20-q for a product, where p represents price per unit in dollars and q represents the number of units per unit of time, find the equilibrium point. The equilibrium point is square (Type an ordered pair,using integers or fractions.Type an exact answer using radicals as needed.)
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4.5
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Nihat
Elit · 8 yıl öğretmeni
Uzman doğrulaması
Cevap
To find the equilibrium point, we need to set the supply equation equal to the demand equation and solve for q.Given:Supply equation:
Demand equation:
Step 1: Set the supply equation equal to the demand equation.
Step 2: Square both sides of the equation to eliminate the square root.
Step 3: Solve the quadratic equation using the quadratic formula.
Step 4: Calculate the two possible values for q.
Step 5: Substitute the values of q into either the supply or demand equation to find the corresponding values of p.For
:
For
:
Therefore, the equilibrium points are:
and
The equilibrium point is
or
.