Question

A company that manufactures mountain bikes makes a daily profit p according to the equation p equals negative 100 x squared plus 4900 x minus 57 comma 424​, where p is measured in dollars and x is the number of mountain bikes made per day. Find the number of mountain bikes that must be made each day to produce a zero profit for the company.

Answer 1

x is approximately 9 or 58.

Explanation:

p = -100x^{2} + 4900x - 57,424

to find x, when p = 0

0 = -100x^{2} + 4900x - 57,424

Using the almighty formular

x = (-b ± √b^2 - 4ac)/2a

x = (-4900 ± √(4900)^2 - 4 (-100)(-57,424)/2(-100)

x = (-4900 ± √24010000+22969600)/-200

x = (-4900 ± √46979600)/-200

x = (-4900 ± 6854.2)/-200

x = (-4900 + 6854.2)/-200 or x = (-4900 - 6854.2)/-200

x = -9.7 or 58.7

x is approximately 9 or 58.