a company makes and sells charm bracelets. the cost of producing x bracelets is represented by the function…

a company makes and sells charm bracelets. the cost of producing x bracelets is represented by the function c(x)=180 + 8x. the revenue earned from selling x bracelets is represented by the function r(x)=20x. write and simplify a function p that represents the profit made from selling x bracelets. how many bracelets must the company sell to break even?

a company makes and sells charm bracelets. the cost of producing x bracelets is represented by the function c(x)=180 + 8x. the revenue earned from selling x bracelets is represented by the function r(x)=20x. write and simplify a function p that represents the profit made from selling x bracelets. how many bracelets must the company sell to break even?

Answer

Explanation:

Step1: Recall profit - revenue - cost formula

Profit $P(x)=R(x)-C(x)$. Given $C(x) = 180 + 8x$ and $R(x)=20x$, then $P(x)=20x-(180 + 8x)$.

Step2: Simplify the profit function

$P(x)=20x-180 - 8x=12x-180$.

Step3: Find the break - even point

At the break - even point, $P(x) = 0$. So we set $12x-180 = 0$. Add 180 to both sides: $12x=180$. Divide both sides by 12: $x=\frac{180}{12}=15$.

Answer:

The profit function is $P(x)=12x - 180$. The company must sell 15 bracelets to break even.