A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is $3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be chosen in order to break even at the end of the month?
The sale price must be $5.00 per unit in order to break even at the end of the month. This is calculated by taking the fixed cost of $100,000 and dividing it by the number of units (50,000) to get the variable cost per unit ($2.00). Then, add the variable cost per unit ($3.00) to the fixed cost per unit ($2.00) to get the total cost per unit ($5.00).
To break even at the end of the month, the total revenue must equal the total cost.
The fixed cost is $100,000.
The variable cost per unit is $3.00, and the number of units sold is 50,000.
To find the total variable cost, multiply the variable cost per unit by the number of units sold: $3.00 × 50,000 = $150,000.
Therefore, the total cost is the sum of the fixed cost and the total variable cost: $100,000 + $150,000 = $250,000.
To find the sale price that must be chosen to break even, divide the total cost by the number of units sold: $250,000 ÷ 50,000 = $5.00.
Thus, the sale price that must be chosen in order to break even at the end of the month is $5.00 per unit of toothpaste.
To determine the sale price needed to break even, we need to calculate the total cost and total revenue.
First, let's calculate the total cost:
Fixed Cost = $100,000
Variable Cost per unit = $3.00
Number of units = 50,000
Total Cost = Fixed Cost + (Variable Cost per unit * Number of units)
= $100,000 + ($3.00 * 50,000)
= $100,000 + $150,000
= $250,000
Now, let's calculate the break-even revenue. At the break-even point, the total revenue is equal to the total cost.
Total Revenue = Total Cost
Sale Price per unit * Number of units = Total Cost
Sale Price per unit = Total Cost / Number of units
= $250,000 / 50,000
= $5.00
Therefore, the sale price per unit of toothpaste must be set at $5.00 in order to break even at the end of the month.