Question #9c650

Question

1308 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-08T18:13:01

See explanation below:

To break even the cost to produce the product, $c (x)$ $c(x)$ , must equal the revenue generated by selling the product, $r (x)$ $r(x)$ . Therefore,

$c (x) = r (x)$ $c(x) = r(x)$

or

$5 x + 18 = 2 x^{2}$ $5x + 18 = 2x^2$

We can now solve this for $x$ $x$ .

$5 x + 18 - 5 x - 18 = 2 x^{2} - 5 x - 18$ $5x + 18 - color(red)(5x) - color(blue)(18) = 2x^2 - color(red)(5x) - color(blue)(18)$

$5 x - 5 x + 18 - 18 = 2 x^{2} - 5 x - 18$ $5x - color(red)(5x) + 18 - color(blue)(18) = 2x^2 - color(red)(5x) - color(blue)(18)$

$0 + 0 = 2 x^{2} - 5 x - 18$ $0 + 0 = 2x^2 - 5x - 18$

$0 = 2 x^{2} - 5 x - 18$ $0 = 2x^2 - 5x - 18$

We can now factor this.

$2 x^{2} - 5 x - 18 = 0$ $2x^2 - 5x - 18 = 0$

$(2 x - 9) (x + 2) = 0$ $(2x - 9)(x + 2) = 0$

We can now solve both of these for $0$ $0$ :

$2 x - 9 = 0$ $2x - 9 = 0$

$2 x - 9 + 9 = 0 + 9$ $2x - 9 + 9 = 0 + 9$

$2 x - 0 = 9$ $2x - 0 = 9$

$2 x = 9$ $2x = 9$

$\frac{2 x}{2} = \frac{9}{2}$ $(2x)/2 = 9/2$

$x = \frac{9}{2}$ $x = 9/2$

and

$x + 2 = 0$ $x + 2 = 0$

$x + 2 - 2 = 0 - 2$ $x + 2 - 2 = 0 - 2$

$x + 0 = - 2$ $x + 0 = -2$

$x = - 2$ $x = -2$

Because you can't produce NEGATIVE units the answer is 9/2 or 4.5 units are needed to be produced to break even.

But because you can't create a 1/2 a unit you need to round up to 5 units.