Question

If the supply and demand functions for a commodity are given by 2p - q + 10 = 0 and (p + q)(q + 10) = 3642 respectively, find the equilibrium price and quantity that give market equilibrium. (Round your answers to two decimal places.)
Equilibrium price =

Answer 1

well, as I recall, the equilibrium price and quantity are where supply equals demand. So, we want

2p-q+10 = (p+q)(q+10)-3642
since q = 2p+10, that means

(p+2p+10)(2p+10+10) = 3642
6p^2+80p-3442 = 0
p = 18.195
so, q = 46.390

Check:
2(18.195)-46.390 +10 = 0
(18.195+46.390)(56.390) = 3642

The curves are at

http://www.wolframalpha.com/input/?i=plot+2p+-+q+%2B+10+%3D+0+and+%28p+%2B+q%29%28q+%2B+10%29+%3D+3642+for+p+%3D+0+to+50