sam sells necklaces for 10 dollars each. each necklace cost her 5 dollars to make.she also has 5,000 dollars in fixed costs per year for her jewelry business. how many necklaces must she sell in order to make a profit of 1,000 dollars in one year
profit=revenue-expense
= 10N-5N-5000=5N-5000
if she makes 1000 per year, then
1000=5N-5000
solve for N
To determine how many necklaces Sam must sell in order to make a profit of $1,000 in one year, we need to consider her costs and revenue.
Let's break it down step by step:
1. Calculate Sam's total variable cost per necklace:
The cost to make each necklace is $5. Since each necklace has a fixed cost of $5, Sam's total variable cost per necklace is $5.
2. Calculate Sam's revenue per necklace:
Sam sells each necklace for $10.
3. Calculate Sam's total fixed costs per year:
Sam has $5,000 in fixed costs per year.
4. Calculate Sam's total variable costs per year:
Since the variable cost per necklace is $5 and we want to find the number of necklaces Sam needs to sell to make a profit of $1,000, we'll denote the number of necklaces as x. Therefore, the total variable cost per year is 5 * x.
5. Calculate Sam's total costs per year:
Sam's total costs per year are the sum of the fixed costs and the variable costs:
Total costs per year = Total fixed costs per year + Total variable costs per year
Total costs per year = $5,000 + (5 * x)
6. Calculate Sam's total revenue per year:
Sam's total revenue per year is the revenue per necklace multiplied by the number of necklaces sold, which we will denote as x:
Total revenue per year = Revenue per necklace * Number of necklaces sold
Total revenue per year = $10 * x
7. Set up the equation for Sam's profit:
Profit = Revenue - Costs
Since Sam wants to make a profit of $1,000, we have:
$1,000 = Total revenue per year - Total costs per year
8. Substitute the calculated values into the equation:
$1,000 = ($10 * x) - ($5,000 + 5 * x)
9. Simplify the equation:
$1,000 = $10x - $5,000 - $5x
10. Combine like terms:
$1,000 = $5x - $5,000
11. Move the constant term to the right side of the equation:
$5x = $1,000 + $5,000
$5x = $6,000
12. Solve for x:
x = $6,000 / $5
x = 1,200
Therefore, Sam must sell 1,200 necklaces in order to make a profit of $1,000 in one year.