Question

# The company produces a product with a variable cost of $90 per unit. With fixed costs of$150,000 and a selling price of $1,200 per item, how many units must be sold to achieve a profit of$400,000?

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## Answer to a math question The company produces a product with a variable cost of $90 per unit. With fixed costs of$150,000 and a selling price of $1,200 per item, how many units must be sold to achieve a profit of$400,000?

Timmothy
4.8
To find out how many units must be sold to achieve a profit of $400,000, we need to set up the profit equation. Let's denote the number of units sold as$x$. The total cost can be calculated by taking the sum of the fixed costs $150,000$ and variable costs per unit $90$ multiplied by the number of units sold $$x$$: Total cost = Fixed costs + $Variable cost per unit * Number of units sold$ = 150,000 + $90 *$x$
The total revenue can be calculated by multiplying the selling price per unit $1,200$ by the number of units sold $$x$$: Total revenue = Selling price per unit * Number of units sold = 1,200 * $x The profit can be calculated by subtracting the total cost from the total revenue: Profit = Total revenue - Total cost Now we can set up the equation to find the number of units sold: 1,200x - $150,000 + 90x$ = 400,000 To solve this equation, we can first simplify it: 1,200x - 150,000 - 90x = 400,000 Combining like terms: 1,200x - 90x - 150,000 = 400,000 1,110x - 150,000 = 400,000 Next, we can isolate the variable on one side: 1,110x = 400,000 + 150,000 1,110x = 550,000 Dividing both sides by$$1,110: x = \frac{550,000}{1,110} Simplifying: x \approx 494.59 Therefore, approximately 494.59 units must be sold to achieve a profit of$400,000.
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