A video game manufacturer is planning to market a new machine. The fixed costs are $550,000 and the variable costs are $120 per machine. The wholesale price of the machine will be $140. How many game machines must be sold for the company to make a profit?
my answer was 27,500 it is wrong
140n = 550,000 + 120n
20n = 550,000
n = 27,500
I don't know why it's wrong, unless the answer key is wrong (which happens every once in a while) or you have a typo above.
27500
To determine the number of game machines that need to be sold for the company to make a profit, we need to calculate the break-even point. The break-even point is the quantity at which the total revenue equals the total cost, resulting in zero profit or loss.
Let's break down the costs involved:
Fixed costs: $550,000
Variable costs: $120 per machine
Wholesale price: $140 per machine
To find the break-even point, we need to set up an equation where the total revenue equals the total cost.
Let's assume the number of game machines sold is 'x'. The total revenue is calculated by multiplying the wholesale price per machine by the quantity sold, while the total cost consists of both fixed costs and variable costs.
Total Revenue = Wholesale Price x Quantity Sold
Total Cost = Fixed Costs + (Variable Costs per Machine x Quantity Sold)
Setting these two equations equal, we can find the break-even point:
140x = 550,000 + (120x)
Simplifying the equation:
140x - 120x = 550,000
20x = 550,000
x = 550,000 / 20
x = 27,500
So, to make a profit, the company needs to sell more than 27,500 game machines. Your answer of 27,500 is correct.