A business has fixed costs of $3,570 per month and the product sells for $105. The variable cost is $26 per unit.The business wishes to make a profit of $4,227 AFTER tax.How many units must be sold? Answer in whole units only.
Question
A business has fixed costs of 105. The variable cost is 4,227 AFTER tax.How many units must be sold? Answer in whole units only.
Solution
To solve this problem, we first need to understand the basic profit equation which is:
Profit = Total Revenue - Total Cost
Where:
- Total Revenue = Price per unit * Quantity sold
- Total Cost = Fixed Cost + Variable Cost * Quantity sold
We know that the business wants to make a profit of $4,227 after tax. However, we don't have the tax rate. Assuming the profit mentioned is after considering the tax, we can use the profit figure directly.
So, we can set up the equation as follows:
105 * Quantity sold) - (26 * Quantity sold)
Solving this equation will give us the number of units that must be sold.
First, simplify the equation:
105Q - 26Q
Combine like terms:
79Q - $3,570
Add $3,570 to both sides:
3,570 = $79Q
79Q
Finally, divide both sides by $79 to solve for Q:
Q = 79
Q = 98.69 units
Since we can't sell a fraction of a unit, we'll need to round up to the nearest whole unit. So, the business needs to sell 99 units to achieve a profit of $4,227 after tax.
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