calculus for Business

Question

The weekly demand and supply functions for new iPhone cases are given by

p= -0.2x^2-x+60

p= 0.1x^2+3x+20

respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity and price, using correct units in your answers and rounding to the nearest whole number.

Answer 1

-2x^2 -10x +600 = x^2 +30x +200

3x^2 +40x -400 = 0

x=-40/6 + or - (1/6)sqr(1600+4800))

x= 40/6 = 20/3 = 7 as the nearest whole number

x = 7 hundreds = 700= equilibrium quantity

p= (20/3)^2 +30(20/3) +200 = 400/9 + 200+200 = 400+44.44. = $444 = equilibrium price rounded to nearest integer