SOLUTION: Find the equilibrium point, if p is the price per unit, and q represents the number of units per unit of time. Supply: p=(1/4)q+6, Demand: p=2240/(q+12). Thank you!

Question 1056056: Find the equilibrium point, if p is the price per unit, and q represents the number of units per unit of time. Supply: p=(1/4)q+6, Demand: p=2240/(q+12). Thank you!
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Set the two equal to each other
(1/4)q+6=2240/(q+12)
multiply both sides by (q+12)
(1/4)q^2+3q+6q+72=2240
(1/4)q^2+9q+72=2240
(1/4)q^2+9q-2168=0; multiply by 4.
q^2+36q-8672=0
discriminant is sqrt(1296+34688)=sqrt(35984)=189.69
q=(1/2)(-36+189.69) since these can't be negative
q=76.85
Check (1/4)(76.85)+6=25.21=p
2240/(88.85)=25.21=p
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