A yo-yo factory has fixed operating costs of $450,000 per year. In addition to the fixed costs, the cost to produce one yo-yo is $1.10. The yo-yo company sells the yo-yos to a distributor for $5.50 each. How many yo-yos must be sold in a year to earn a profit of at least $140,000?
To determine the number of yo-yos that must be sold in a year to earn a profit of at least $140,000, we need to consider both the fixed costs and the variable costs associated with producing yo-yos.
Let's break down the costs:
Fixed Operating Costs = $450,000 per year
Cost to Produce One Yo-yo = $1.10
Selling Price to Distributor = $5.50
To calculate the profit, we subtract the total costs from the total revenue:
Profit = Total Revenue - Total Costs
The total revenue is the selling price multiplied by the number of yo-yos sold, and the total costs include the fixed costs and the variable costs.
Let's assume the number of yo-yos sold in a year is represented by "n."
Total Revenue = Selling Price x Number of Yo-yos Sold
Total Costs = Fixed Operating Costs + (Variable Cost per Yo-yo x Number of Yo-yos Sold)
Now, we can set up the equation to solve for "n":
Profit >= Total Revenue - Total Costs
$140,000 >= ($5.50 x n) - ($1.10 x n + $450,000)
Simplifying the equation:
$140,000 >= $4.40n - $1.10n - $450,000
$140,000 >= $3.30n - $450,000
Moving the variables to one side and the constant terms to the other side:
$3.30n >= $140,000 + $450,000
$3.30n >= $590,000
Dividing both sides of the inequality by $3.30 to solve for "n":
n >= $590,000 / $3.30
n >= 178,787.88
Since the number of yo-yos sold must be a whole number, the minimum number of yo-yos that must be sold in a year to earn a profit of at least $140,000 is 178,788 yo-yos.
fixed op+ making = 450001.10
profit per yoyo = 4.40
profit earned total is 140000
let there are x yoyo's sold
x*5.50= 450001.10+140000
x = 590001.10/5.50