The weekly demand and supply functions for sportsman 5 * 7 tents are given by p = - 0.1x2 - x + 44 p = 0.1x2 + 2x + 24 respectively, where p is measured in dollars and x is measured in units of a hundred. find the equilibrium quantity. hundred units

Given supply and demand functions

p1 (x) = - 0.1x2 - x + 44 (demand)

p2 (x) = 0.1x2 + 2x + 24 (supply)

At equilibrium, demand equals supply, hence

p1 (x) = p2 (x) = >

-0.1x^2-x+44 = 0.1x^2+2x+24

rearrange

0.2x^2+3x-20=0 = > x^2+15x-100

Solve for x using the quadratic formula:

x = (-15 ± sqrt (625)) / 2=-7.5 ± 12.5

reject negative root to give x=5