Find the break-even point for the following. Draw your own graph on a piece of paper.
Fixed cost = $20,000
Variables cost = $13 per item
Price = $23
you want x such that the cost = the revenue. That is,
20000+13x = 23x
To find the break-even point, we need to determine the quantity of items that need to be sold in order to cover the total costs. The break-even point is the point at which total cost equals total revenue.
Let's start by calculating the total cost and total revenue.
Total cost = Fixed cost + (Variable cost per item * quantity)
Total cost = $20,000 + ($13 * quantity)
Total revenue = Price per item * quantity
Total revenue = $23 * quantity
To find the break-even point, we set the total cost equal to the total revenue:
$20,000 + ($13 * quantity) = $23 * quantity
Now, let's solve this equation:
$20,000 + $13 * quantity = $23 * quantity
First, subtract $13 * quantity from both sides of the equation:
$20,000 = $23 * quantity - $13 * quantity
Combine like terms:
$20,000 = $10 * quantity
Now, divide both sides of the equation by $10:
$20,000 / $10 = quantity
(quantity) = 2,000
Therefore, the break-even point is 2,000 items.
Now, let's draw a graph on a piece of paper to visualize this.
On the x-axis, we can mark the quantity of items sold, ranging from 0 to 3,000. On the y-axis, we can mark the total costs and total revenue, ranging from 0 to $40,000.
First, plot the total cost line:
- When the quantity is 0, the total cost is $20,000.
- When the quantity is 2,000, the total cost becomes $20,000 + ($13 * 2,000) = $46,000.
Next, plot the total revenue line:
- When the quantity is 0, the total revenue is $0.
- When the quantity is 2,000, the total revenue becomes $23 * 2,000 = $46,000.
Finally, draw a line representing the break-even point where the total cost line intersects with the total revenue line at the quantity of 2,000 items.
This graph will give you a visual representation of the break-even point.