A company has a fixed monthly manufacturing cost of $12,000 and it costs $0.95 to produce a mechanical pencil. They then sell each pencil for $1.25. How many units must be sold before this company breaks even?

cost = revenue

to break even

So, what is the cost for x pencils?

To determine the number of units that need to be sold for the company to break even, we need to consider the fixed monthly manufacturing cost and the cost and selling price of each mechanical pencil.

Let's break down the costs and revenue involved:

Fixed monthly manufacturing cost: $12,000
Cost to produce a mechanical pencil: $0.95
Selling price of each pencil: $1.25

To calculate the break-even point, we need to find the number of units that cover both the variable cost (cost to produce each pencil) and the fixed cost.

Let's denote the number of units as 'x'. The total cost (TC) is the sum of the fixed cost (FC) and the variable cost per unit (VC):

TC = FC + (VC per unit * x)

Substituting the values:
TC = $12,000 + ($0.95 * x)

The revenue (R) is the selling price per unit (SP) multiplied by the number of units (x):

R = SP per unit * x

Substituting the values:
R = $1.25 * x

The company breaks even when the total cost equals the revenue:

TC = R
$12,000 + ($0.95 * x) = $1.25 * x

To solve for x, we can rearrange the equation:

$0.95 * x - $1.25 * x = -$12,000
($0.95 - $1.25) * x = -$12,000
-$0.30 * x = -$12,000
x = -$12,000 / -$0.30
x = 40,000

Therefore, the company must sell 40,000 mechanical pencils to break even.