Question

a company makes a profit when it brings in more money than it pays out. suppose a companys revenue (the amount brought in) can be modeled by $r = 170x$, and its costs (the amount paid out) can be modeled by $c = 150x + 23700$, where $x$ is the number of items sold. how many items must be sold for the company to make a profit? (hint: round up to the next whole value of items to make sure of a profit...breaking even is not a profit.) the company must sell select an answer items. in interval notation, this is written . > next question

Explanation:

Step1: Set up profit inequality

Profit occurs when revenue > cost, so:
$170x > 150x + 23700$

Step2: Isolate x term

Subtract $150x$ from both sides:
$170x - 150x > 23700$
$20x > 23700$

Step3: Solve for x

Divide both sides by 20:
$x > \frac{23700}{20}$
$x > 1185$

Step4: Round up to whole item

Since $x$ must be an integer and breaking even is not profit, we round up to the next whole number.

Answer:

The company must sell 1186 items.
In interval notation, this is written $(1185, \infty)$.