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?

Keep answer simple

Answer 1

the company must sell 15 bracelets to break even.

Explanation:

To find the profit made from selling x bracelets, we need to subtract the cost of producing x bracelets from the revenue earned from selling x bracelets.

The cost of producing x bracelets is given by the function C(x) = 180 + 8x.

The revenue earned from selling x bracelets is given by the function R(x) = 20x.

To find the profit, we subtract the cost from the revenue: P(x) = R(x) - C(x).

Substituting the given functions:

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

To simplify the expression, we combine like terms:

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

Simplifying further, we combine the x terms and the constant terms:

P(x) = 12x - 180.

So, the function P(x) represents the profit made from selling x bracelets: P(x) = 12x - 180.

To find the number of bracelets the company must sell to break even, we set the profit (P(x)) equal to zero, since profit is zero at the break-even point:

12x - 180 = 0.

Adding 180 to both sides of the equation:

12x = 180.

Dividing both sides by 12:

x = 15.