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
56000+9x = 16x
To find the break-even point algebraically, we need to determine the number of units that need to be sold in order to cover both the fixed costs and the variable costs.
Let x represent the number of units sold.
The total cost (TC) can be calculated as follows:
TC = Fixed Costs + Variable Costs
Fixed Costs = $56,000
Variable Costs = Cost per unit x Number of units
= $9x
TC = $56,000 + $9x
The total revenue (TR) can be calculated as:
TR = Price per unit x Number of units
= $16x
The break-even point occurs when the total cost equals total revenue. Therefore, we can set up the equation:
TC = TR
$56,000 + $9x = $16x
To isolate x, we can subtract $9x from both sides of the equation:
$56,000 = $16x - $9x
$56,000 = $7x
x = $56,000 / $7
x = 8,000
Therefore, the break-even production is 8,000 units.
To calculate the break-even revenue, we can substitute the value of x into the total revenue equation:
TR = $16 x 8,000
TR = $128,000
Therefore, the break-even revenue is $128,000.
Thus, the correct answer is option c. break-even production 8,000 units; break-even revenue $128,000.
To find the break-even point algebraically, we need to determine the production quantity at which the total cost equals the total revenue.
Let's break down the costs and revenue involved here:
Fixed Cost (FC): $56,000
Variable Cost per Unit (VC): $9
Selling Price per Unit (SP): $16
Total Cost (TC) = Fixed Cost + (Variable Cost per Unit * Quantity)
Total Revenue (TR) = Selling Price per Unit * Quantity
To find the break-even point, we need to set TC equal to TR and solve for the quantity.
TC = TR
To substitute the values:
$56,000 + ($9 * Quantity) = $16 * Quantity
Simplify the equation:
$56,000 + $9 * Quantity = $16 * Quantity
Subtract $9 * Quantity from both sides:
$56,000 = $16 * Quantity - $9 * Quantity
Combine like terms on the right side:
$56,000 = $7 * Quantity
To solve for Quantity, divide both sides by $7:
Quantity = $56,000 / $7
Quantity = 8,000 units
So, the break-even production is 8,000 units. To find the break-even revenue, multiply the break-even production by the selling price per unit:
Break-even revenue = 8,000 units * $16 = $128,000
Hence, the correct answer is option c: break-even production 8,000 units; break-even revenue $128,000.