Question

handmade candles
april sells handmade candles at a local market and wants to analyze
the business’s financial situation.
cost: $c(x) = 3x + 50$
revenue: $r(x) = -x^2 + 30x$
what are the break - even points?
$(2, 56)$ and $(25, 125)$
$(0, 0)$ and $(2, 56)$
$(2, 56)$ and $(15, 225)$

Explanation:

Step1: Set cost equal to revenue

$C(x) = R(x)$
$3x + 50 = -x^2 + 30x$

Step2: Rearrange to quadratic equation

$x^2 - 27x + 50 = 0$

Step3: Solve the quadratic equation

Factor: $(x-2)(x-25)=0$
Solutions: $x=2$ and $x=25$

Step4: Find corresponding y-values

For $x=2$: $C(2)=3(2)+50=56$
For $x=25$: $C(25)=3(25)+50=125$

Answer:

(2, 56) and (25, 125)