Can someone help me with this Math problem?
A Company plans to market a new model of house. Based on its
market studies, the company estimates that it can sell up to 3,500 units in 2019.
The selling price will be $2,000,000/unit. Variable costs are estimated to
be 40% of total revenue and fixed costs are estimated to be $16,000,000 for 2019.
Determine if the company can sell enough units to break even?
for break even ... u * (1 - .40) * 2000000 = (u * .40 * 2000000) + 16000000
u * .20 * 2000000 = 16000000
To determine if the company can sell enough units to break even, we need to calculate the total costs and total revenue.
1. Calculate the total costs:
Fixed costs: $16,000,000
Variable costs: 40% of total revenue
2. Calculate the total revenue:
Selling price per unit: $2,000,000
Number of units sold: 3,500
Now let's calculate the total costs and total revenue:
1. Total Costs:
Variable costs = 40% * total revenue
2. Total Revenue:
Total revenue = selling price per unit * number of units sold
3. Break-even point:
Break-even point is the point at which total revenue equals total costs. If the company sells enough units to cover all costs, it has reached the break-even point.
So, we need to compare the total costs and total revenue.
Now let's calculate:
1. Total Costs:
Variable costs = 40% * total revenue
Variable costs = 0.4 * (selling price per unit * number of units sold)
2. Total Revenue:
Total revenue = selling price per unit * number of units sold
3. Break-even point:
If total revenue >= total costs, the company has reached the break-even point.
Let's plug in the values:
Variable costs = 0.4 * ($2,000,000 * 3,500)
Variable costs = 0.4 * $7,000,000,000
Variable costs = $2,800,000,000
Total costs = Fixed costs + Variable costs
Total costs = $16,000,000 + $2,800,000,000
Total costs = $2,816,000,000
Total revenue = $2,000,000 * 3,500
Total revenue = $7,000,000,000
Therefore,
Total revenue = $7,000,000,000
Total costs = $2,816,000,000
Since total revenue ($7,000,000,000) is greater than total costs ($2,816,000,000), the company can sell enough units to break even.