Answer:
x = 20
x = 140
Step-by-step explanation:
Find the equation for profit P
P = R - C
Substitute the equations for R and C then simplify.
P = 100x − 0.5x² - (20x + 700)
P = -0.5x² + 80x - 700
Find the values of x when profit is $700
P = -0.5x² + 80x - 700
700 = -0.5x² + 80x - 700
0 = -0.5x² + 80x - 1400
This is in the standard form 0 = ax² + bx + c
Use the quadratic formula to find values of x
[tex]x = \frac{-b±\sqrt{b^{2}-4ac} }{2a}[/tex]
(Ignore Â)
Substitute a b and c.
a = -0.5
b = 80
c = -1400
[tex]x = \frac{-(80)±\sqrt{80^{2}-4(-0.5)(-1400)} }{2(-0.5)}[/tex]
[tex]x = \frac{-80±60}{-1}[/tex]
Split the formula at the ± so that there are two to get the two x values.
[tex]x = \frac{-80+60}{-1}[/tex]
[tex]x = \frac{-80-60}{-1}[/tex]
x = 20
x = 140
The profit will be $700 when x is 20 or when x is 140.
