Question

the cost in dollars to produce x cups of lemonade is represented by the function $c(x)=10 + 0.20x$. the revenue in dollars earned by selling x cups of lemonade is represented by the function $r(x)=0.50x$. what is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?
○ 33 cups
○ 33.33 cups
○ 33.67 cups
○ 34 cups

Explanation:

Step1: Set revenue > cost

$0.50x > 10 + 0.20x$

Step2: Isolate x terms

$0.50x - 0.20x > 10$
$0.30x > 10$

Step3: Solve for x

$x > \frac{10}{0.30}$
$x > 33.\overline{3}$

Step4: Round to whole cups

Since x must be a whole number greater than $33.\overline{3}$, we round up to 34.

Answer:

34 cups