The owner of a bike shop that produces custom built bike frames has determined that the demand equation for bike frames is given by the equation
d(q) = –6.10q^2 –5q + 1000
where d(q) is the price in dollars and q is the number of bike frames demanded per week. the supply equation for bike frames is
s(q) = 3.20q^2 + 10q – 80
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.

equilibrium point (10,340)

Step-by-step explanation:

To find the equilibrium point, equal the demand and the supply:

Reorganize the terms in one side and reduce similar terms:

that's a cuadratic equation, solve with the general formula when:

a=9.3, b=15, c=-1080

q can't be negative because it is the quantity of bike frames, so:

This value of q can't be considered.

Then substitute the value of q in D(q) to find the price p:

The equilibrium point (q,p) is (10,340).

step-by-step explanation:

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