Sandra Makes And Sells Bracelets. It Costs Her $$ 2$ To Make Each Bracelet, Plus A One-time Cost Of $$ 15$ For Supplies. She Plans To Sell Each Bracelet For $$ 5$. Let $x$ Represent The
Introduction
Sandra is an entrepreneur who has started a small business selling handmade bracelets. To understand the profitability of her business, we need to analyze the costs involved in making and selling each bracelet. In this article, we will use mathematical concepts to determine the break-even point, revenue, and profit of Sandra's bracelet business.
Costs and Revenue
Sandra incurs two types of costs: the cost of making each bracelet and a one-time cost for supplies. The cost of making each bracelet is $2, and the one-time cost for supplies is $15. She plans to sell each bracelet for $5.
Cost of Making Each Bracelet
The cost of making each bracelet is a fixed cost that Sandra incurs for each unit sold. This cost is represented by the variable , which is equal to $2 in this case.
One-Time Cost for Supplies
The one-time cost for supplies is a fixed cost that Sandra incurs only once, regardless of the number of bracelets she sells. This cost is represented by the variable , which is equal to $15 in this case.
Selling Price of Each Bracelet
The selling price of each bracelet is the price at which Sandra sells each unit. This price is represented by the variable , which is equal to $5 in this case.
Break-Even Point
The break-even point is the point at which Sandra's total revenue equals her total cost. To find the break-even point, we need to calculate the total revenue and total cost.
Total Revenue
The total revenue is the total amount of money Sandra earns from selling each bracelet. This is calculated by multiplying the selling price of each bracelet by the number of bracelets sold.
Total Revenue = Number of Bracelets Sold × Selling Price of Each Bracelet = x × $5 = $5x
Total Cost
The total cost is the sum of the cost of making each bracelet and the one-time cost for supplies. This is calculated by multiplying the cost of making each bracelet by the number of bracelets sold and adding the one-time cost for supplies.
Total Cost = (Cost of Making Each Bracelet × Number of Bracelets Sold) + One-Time Cost for Supplies = (2x + 15)
Break-Even Point Equation
The break-even point is the point at which the total revenue equals the total cost. This is represented by the equation:
Total Revenue = Total Cost $5x = 2x + 15
Solving the Break-Even Point Equation
To find the break-even point, we need to solve the equation:
$5x = 2x + 15
Subtracting 2x from both sides gives:
$3x = 15
Dividing both sides by 3 gives:
x = 5
This means that Sandra needs to sell at least 5 bracelets to break even.
Revenue and Profit
Once Sandra has sold enough bracelets to break even, she can start making a profit. The profit is the difference between the total revenue and the total cost.
Total Revenue
The total revenue is the total amount of money Sandra earns from selling each bracelet. This is calculated by multiplying the selling price of each bracelet by the number of bracelets sold.
Total Revenue = Number of Bracelets Sold × Selling Price of Each Bracelet = x × $5 = $5x
Total Cost
The total cost is the sum of the cost of making each bracelet and the one-time cost for supplies. This is calculated by multiplying the cost of making each bracelet by the number of bracelets sold and adding the one-time cost for supplies.
Total Cost = (Cost of Making Each Bracelet × Number of Bracelets Sold) + One-Time Cost for Supplies = (2x + 15)
Profit
The profit is the difference between the total revenue and the total cost.
Profit = Total Revenue - Total Cost = $5x - (2x + 15) = $3x - 15
Profit per Bracelet
The profit per bracelet is the profit divided by the number of bracelets sold.
Profit per Bracelet = Profit ÷ Number of Bracelets Sold = ($3x - 15) ÷ x = $3 - 15/x
Maximum Profit
The maximum profit occurs when the number of bracelets sold is at its maximum. This is represented by the equation:
Maximum Profit = Profit per Bracelet × Number of Bracelets Sold = ($3 - 15/x) × x = $3x - 15
This means that the maximum profit is $3x - 15.
Conclusion
In conclusion, Sandra's bracelet business has a break-even point of 5 bracelets. Once she has sold enough bracelets to break even, she can start making a profit. The profit is the difference between the total revenue and the total cost. The profit per bracelet is the profit divided by the number of bracelets sold. The maximum profit occurs when the number of bracelets sold is at its maximum.
Recommendations
Based on the analysis, we can make the following recommendations:
- Sandra should aim to sell at least 5 bracelets to break even.
- Once she has sold enough bracelets to break even, she can start making a profit.
- The profit per bracelet is $3 - 15/x, which means that the profit per bracelet increases as the number of bracelets sold increases.
- The maximum profit is $3x - 15, which means that the maximum profit increases as the number of bracelets sold increases.
Introduction
In our previous article, we analyzed the costs and revenue of Sandra's bracelet business and determined the break-even point, revenue, and profit. In this article, we will answer some frequently asked questions about Sandra's bracelet business.
Q&A
Q: What is the break-even point for Sandra's bracelet business?
A: The break-even point for Sandra's bracelet business is 5 bracelets. This means that Sandra needs to sell at least 5 bracelets to break even.
Q: How much profit will Sandra make if she sells 10 bracelets?
A: To calculate the profit, we need to calculate the total revenue and total cost. The total revenue is $5x, where x is the number of bracelets sold. The total cost is (2x + 15), where x is the number of bracelets sold. The profit is the difference between the total revenue and the total cost.
Profit = Total Revenue - Total Cost = $5x - (2x + 15) = $3x - 15
If Sandra sells 10 bracelets, the profit will be:
Profit = $3(10) - 15 = $30 - 15 = $15
Q: What is the profit per bracelet if Sandra sells 10 bracelets?
A: The profit per bracelet is the profit divided by the number of bracelets sold.
Profit per Bracelet = Profit ÷ Number of Bracelets Sold = ($3x - 15) ÷ x = $3 - 15/x
If Sandra sells 10 bracelets, the profit per bracelet will be:
Profit per Bracelet = $3 - 15/10 = $3 - 1.5 = $1.5
Q: What is the maximum profit that Sandra can make?
A: The maximum profit occurs when the number of bracelets sold is at its maximum. This is represented by the equation:
Maximum Profit = Profit per Bracelet × Number of Bracelets Sold = ($3 - 15/x) × x = $3x - 15
This means that the maximum profit is $3x - 15.
Q: How can Sandra increase her profit?
A: Sandra can increase her profit by selling more bracelets. As the number of bracelets sold increases, the profit per bracelet also increases.
Q: What is the one-time cost for supplies?
A: The one-time cost for supplies is $15.
Q: What is the cost of making each bracelet?
A: The cost of making each bracelet is $2.
Q: What is the selling price of each bracelet?
A: The selling price of each bracelet is $5.
Conclusion
In conclusion, we have answered some frequently asked questions about Sandra's bracelet business. We have determined the break-even point, revenue, and profit, and have provided recommendations for increasing profit. By following these recommendations, Sandra can increase her profit and make her bracelet business more successful.
Recommendations
Based on the analysis, we can make the following recommendations:
- Sandra should aim to sell at least 5 bracelets to break even.
- Once she has sold enough bracelets to break even, she can start making a profit.
- The profit per bracelet is $3 - 15/x, which means that the profit per bracelet increases as the number of bracelets sold increases.
- The maximum profit is $3x - 15, which means that the maximum profit increases as the number of bracelets sold increases.
- Sandra can increase her profit by selling more bracelets.
- The one-time cost for supplies is $15.
- The cost of making each bracelet is $2.
- The selling price of each bracelet is $5.
By following these recommendations, Sandra can increase her profit and make her bracelet business more successful.