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?

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.

Answer: \boxed{494.59 \text{ units}}