Question

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 1

answer for edg2020

Explanation:

Profit is revenue minus cost.

P(x) = R(x) – C(x) or

P(x) = 20x – (180 + 8x)

Distribute and combine like terms.

P(x) = 12x – 180

The breakeven point is when P(x) = 0.

0 = 12x – 180

180 = 12x

x = 15

They must sell 15 bracelets to break even.

Answer 2

Revenue, Cost and Profit are related by the following formula:

Profit = Revenue - Cost

We are given cost and revenue functions:

Cost C(x) = 180 + 8x

Revenue R(x) = 20x

Plugging the values in formula :

Profit = 20x -(180+8x)

let Profit function is P(x)

`P(x) =20x -(180+8x)`

`P(x) =20x -180-8x`

combining like terms

`P(x) =12x -180`

Break Even: It occurs when revenue and cost are equal.

so let us find bracelets sold by company to break even.

Revenue = Cost

`20x = 180+8x`

subtracting 8x from left side

`12x =180`

dividing both sides by 12

x = 180/12

x= 15

So the company must sell 15 bracelets to break even.