The demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.

Question

p = -0.01x^2 - 0.1 x + 47
Determine the consumers' surplus if the market price is set at $5/cartridge. (Round your answer to two decimal places.)

Answer 1

5 = -0.01x^2 - 0.1 x + 47

0.01x^2 +.1x -47+5 = 0

x^2 + 10x -4200=0

(x-60)(x+ 70)=0

x = 60

x = -70

ʃ (−0.01x^2 − 0.1x + 47)dx on [0,60] - 5*60

(-.01/3x^3/3 -.1x^2/2 + 47x on [0,60] - 300

1920-300 = 1620