Question

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?

Answer 1

Answer:

At x = 2 and 10.

Step-by-step explanation:

Given : The cost of producing x hundred items is given by the equation $C(x) = x^2-3x + 7$

The revenue generated from sales of x hundred units is given by the equation $R(x) = -x^2 + 21x-33$

To Find :What values of x will the company break even?

Solution:

Cost function : $C(x) = x^2-3x + 7$

Revenue function : $R(x) = -x^2 + 21x-33$

Now to find the company break even :

$-x^2 + 21x-33= x^2-3x + 7$

$24x= 2x^2+40$

$12x= x^2+20$

$x^2-12x+20=0$

$x^2-10x-2x+20=0$

$x(x-10)-2(x-10)=0$

$(x-2)(x-10)=0$

So, x = 2,10

Hence the company break even at x = 2 and 10.