Question

company revenue
a company’s revenue, $r(x) = -0.4x^2 + 6x$, in thousands of dollars, from selling $x$ thousand units, and its cost, $c(x) = 2x$, thousands of dollars.
how many units must the company sell to break even?
0 or 7,500 units
0 or 10,000 units
7,500 or 10,000 units

Explanation:

Step1: Set revenue equal to cost

$R(x) = C(x)$
$-0.4x^2 + 6x = 2x$

Step2: Rearrange into standard quadratic form

$-0.4x^2 + 6x - 2x = 0$
$-0.4x^2 + 4x = 0$

Step3: Factor the quadratic equation

$x(-0.4x + 4) = 0$

Step4: Solve for x

Substep 4a: Solve $x=0$

$x=0$

Substep 4b: Solve $-0.4x + 4=0$

$-0.4x = -4$
$x = \frac{-4}{-0.4} = 10$

Step5: Convert to actual units

$x$ is in thousands of units, so $x=0$ is 0 units, $x=10$ is $10\times1000=10,000$ units.

Answer:

0 or 10,000 units