Break Even Point

Question

R (x)=200x-2x² 

C (x)=-X² +10x+7425

0< x < 100

Find the number of units that must be produced to break even. 

Answer 1

Set      R(x) = C(x).  Solve for x.

 

200x - 2x² = -x² + 10x + 7425

 

 

Move all the terms to the right side of the equation to make the left side equal to zero.

 

0 = x² - 190x + 7425

 

 

Next, use the quadratic formula to solve for x:

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = -190

c = 7425

 

Plug in these values into the formula.  You should get two x values.  Choose the positive value of x and round to the nearest integer if needed.