The fixed cost to set up a manufacturing business for gizmos is $1200. In addition, each gizmo costs $12 to produce. What is the fewest number of gizmos that a manufacturer must sell at $20 a piece to break even on costs?
To find the fewest number of gizmos that the manufacturer must sell to break even on costs, we need to consider the fixed cost and the variable cost per gizmo.
The fixed cost is given as $1200 and does not change regardless of the number of gizmos produced or sold.
The variable cost per gizmo is $12, which means it costs $12 to produce each gizmo.
To break even on costs, the total revenue from selling the gizmos must be equal to the sum of the fixed cost and the variable cost.
Let's assume the number of gizmos sold is 'x'. The total cost can be expressed as:
Total Cost = Fixed Cost + (Variable Cost per Gizmo * Number of Gizmos)
Total Cost = $1200 + ($12 * x)
The total revenue from selling the gizmos is calculated by multiplying the selling price of each gizmo by the number of gizmos sold. In this case, the selling price is $20.
Total Revenue = Selling Price per Gizmo * Number of Gizmos Sold
Total Revenue = $20 * x
To break even, the total revenue must be equal to the total cost:
Total Revenue = Total Cost
$20 * x = $1200 + ($12 * x)
To find the fewest number of gizmos that need to be sold to break even, we can solve the equation:
$20 * x = $1200 + ($12 * x)
First, let's subtract $12 * x from both sides:
$20 * x - $12 * x = $1200
Simplifying, we get:
$8 * x = $1200
Now, divide both sides by $8:
x = $1200 / $8
x = 150
Therefore, the fewest number of gizmos the manufacturer must sell at $20 each to break even on costs is 150.