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

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

Answer: P(x) = 12x – 180

SOLVINGS

Given:
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.

Explanation of terms:
For x bracelets,
Cost of production is C(x); C(x) = 180 + 8x
Revenue earned is R(x); R(x) = 20x.Profit made is P(x); P(x) is unknown

Profit made = Revenue earned – Cost of production
∴ P(x) = R(x) – C(x)
P(x) = 20x – (180 + 8x)
P(x) = 20x – 180 – 8x
P(x) = 12x – 180

The profit made from selling x bracelets is represented by the function P(x) =
12x – 180