Given the information in the table below, how many units will be required to be sold to hit the break-even point?
| Fixed Cost | $320,000 |
|---|---|
| Variable Cost | $0.80 |
| Selling Price | $4.80 |
[?] units
Answer (2)
Define x as the number of units to be sold.
Express total cost as the sum of fixed cost and variable cost: T o t a lC os t = 320000 + 0.80 x .
Express total revenue as the product of selling price and number of units sold: T o t a lR e v e n u e = 4.80 x .
Set total cost equal to total revenue and solve for x : 320000 + 0.80 x = 4.80 x , which gives x = 80000 . The final answer is 80000 .
Explanation
Understanding the Problem Let's analyze the problem. We are given the fixed costs, variable costs, and selling price of a product. We need to find the number of units that must be sold to cover all costs, which is the break-even point.
Setting up the Equations Let x be the number of units to be sold. The total cost is the sum of the fixed cost and the variable cost, which is given by: T o t a lC os t = F i x e d C os t + ( Va r iab l e C os t × x ) In our case: T o t a lC os t = 320000 + 0.80 x The total revenue is the product of the selling price and the number of units sold: T o t a lR e v e n u e = S e ll in g P r i ce × x In our case: T o t a lR e v e n u e = 4.80 x
Finding the Break-Even Point At the break-even point, the total cost equals the total revenue. Therefore, we set the total cost equal to the total revenue: 320000 + 0.80 x = 4.80 x
Solving for x Now, we solve for x :
Subtract 0.80 x from both sides of the equation: 320000 = 4.80 x − 0.80 x 320000 = 4.00 x Divide both sides by 4.00 :
x = 4.00 320000 x = 80000 Therefore, the break-even point is 80,000 units.
Final Answer Thus, 80,000 units must be sold to reach the break-even point.
Examples
Understanding break-even points is crucial in business. For example, if you're launching a new product, calculating the break-even point helps you determine how many units you need to sell to cover your initial investment and start making a profit. This analysis can guide pricing strategies, production levels, and overall business planning. It ensures that you have a clear target to aim for and can make informed decisions about your resources.
To reach the break-even point, the student needs to sell 80,000 units. This is calculated by setting total costs equal to total revenue. By solving the equation, we find that 80,000 units will cover all costs.
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