The cost of producing x hundred items is given by the equation C(x) = x2 – 3x + 7 and the revenue generated from sales of x hundred units is given by the equation R(x) = –x2 + 21x – 33. What values of x will the company break even?
Accepted Solution
A:
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 = 2,10Hence the company break even at x = 2 and 10.