A manufacturer of 24-hr variable timers, has a monthly fixed cost of $56,000 and a production cost of $9 for each timer manufactured. The units sell for $16 each. Find the break-even point algebraically.



a. break-even production 16,000 units; break-even revenue $1,280,000

b. break-even production 8,000 units; break-even revenue $1,280,000

c. break-even production 8,000 units; break-even revenue $128,000

d. break-even production 16,000 units; break-even revenue $128,000

thank you

Why did the variable timer go on a diet?

Because it wanted to reach its break-even point and slim down those costs!

To find the break-even point algebraically, we need to set the revenue equal to the total cost.

Let's say the number of units produced is x.

The total cost is given by the sum of the fixed cost and the production cost multiplied by the number of units:

Total Cost = Fixed Cost + (Production Cost * Number of Units)

Revenue is given by the selling price multiplied by the number of units:

Revenue = Selling Price * Number of Units

We can set these two equal to find the break-even point:

Fixed Cost + (Production Cost * Number of Units) = Selling Price * Number of Units

$56,000 + ($9 * x) = $16 * x

We can now solve this equation to find the break-even point.

To find the break-even point, we need to determine the number of units that need to be sold to cover all costs, resulting in no profit or loss.

Let's break down the costs involved:
- Monthly fixed cost: $56,000
- Production cost per unit: $9
- Selling price per unit: $16

To calculate the break-even point algebraically, we can use the following formula:

Break-even point = Fixed cost / (Selling price per unit - Variable cost per unit)

First, let's calculate the variable cost per unit:
Variable cost per unit = Production cost per unit = $9

Next, let's calculate the break-even point:
Break-even point = $56,000 / ($16 - $9)
Break-even point = $56,000 / $7
Break-even point = 8,000 units

So, the correct option is:

b. break-even production 8,000 units; break-even revenue $1,280,000

To double-check the break-even revenue, multiply the break-even production (8,000 units) by the selling price per unit ($16):
Break-even revenue = 8,000 units * $16 = $128,000

Therefore, the correct option is:

b. break-even production 8,000 units; break-even revenue $1,280,000.