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

At x = 2 and 10.

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.