Answer:
At x = 2 and 10.
Step-by-step explanation:
Given : The cost of producing x hundred items is given by the equation [tex]C(x) = x^2-3x + 7[/tex]
The revenue generated from sales of x hundred units is given by the equation [tex]R(x) = -x^2 + 21x-33[/tex]
To Find :What values of x will the company break even?
Solution:
Cost function : [tex]C(x) = x^2-3x + 7[/tex]
Revenue function : [tex]R(x) = -x^2 + 21x-33[/tex]
Now to find the company break even :
[tex]-x^2 + 21x-33= x^2-3x + 7[/tex]
[tex]24x= 2x^2+40[/tex]
[tex]12x= x^2+20[/tex]
[tex]x^2-12x+20=0[/tex]
[tex]x^2-10x-2x+20=0[/tex]
[tex]x(x-10)-2(x-10)=0[/tex]
[tex](x-2)(x-10)=0[/tex]
So, x = 2,10
Hence the company break even at x = 2 and 10.
