The demand equation for kitchen ovens is given by the equation
D(q) = –338q + 4,634
where D(q) is the price in dollars and q is the number of kitchen ovens demanded per week. The supply equation for kitchen ovens is
S(q) = 400q^2 + 20
where q is the quantity the supplier will make available per week in the market when the price is p dollars. Find the equilibrium point (q, p) rounded to the nearest hundredth.

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EnigmaRiddle EnigmaRiddle · Answer 1 · 2019-09-17T20:32:35+02:00

Answer:

The equilibrium point is (3, 3620)

Step-by-step explanation:

We set the supply and the demand equation equal to each other and solve:

[tex]-338q+4634=400q^2+20\\400q^2+338q-4614=0[/tex]

We can solve by factoring:

[tex]2(q-3)(200q+769)=0[/tex]

Setting each factor equal to zero we get:

[tex]q=3\text{ or }q=\displaystyle-\frac{769}{200}[/tex]

Only a positive quantity makes sense, so q=3 is the equilibrium quantity.

To get the equilibrium price we just plug 3 in place of q in any of the functions. Let us use the demand function which is easier to handle:

[tex]D(3)=-338(3)+4634=3620[/tex]

Therefore the equilibrium price is p=3620

In ordered pair form the equilibrium point is (3, 3620)