The demand equation for kitchen ovens is given by the equationD(q) = –338q + 4,634where D(q) is the price in dollars and q is the number of kitchen ovens demanded per week. The supply equation for kitchen ovens isS(q) = 400q^2 + 20where 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.

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