Answer:
x=25.61
Step-by-step explanation:
To determine the smallest amount, in dollars , that you can charge and make a profit of atleast $415, you need to find the value of x that gives p=415.
Substitute p=415 in the given quadratic equation and solve it for x.
[tex]415=-0.5x^{2} +36x-179[/tex]
[tex]x^{2} -72x+1188=0[/tex]
[tex]x=\frac{-(-72)+\sqrt{(-72)^{2}-4(1)(1188)} }{2(1)}[/tex]
on solving we get [tex]x=25.61[/tex]
The smallest amount you could charge and make a profit of $415 is $25.61
