SOLUTION: How do I even apprehend this? Can you explain each step for me please. Thanks. If the inventor charges $4 per unit, then her profit for producing and selling x units is given b

You can put this solution on YOUR website!
The profit function for x units is:

To find the profit on 2000 units, just let x = 2000 and substitute into the profit function.
= -2500 This is a loss.
= 4250 This is a profit.
The break-even point is when your sales just cover the cost of production, or in other words, your profit is zero but you don't have a loss.
Set the profit function equal to zero and solve for x.
Solve for x. Add 7000 to both sides of the equation.
Now divide both sides by 2.25

But since you would not make a fraction of a unit, the answer would be rounded to the nearest whole unit, or 3111 units.
The break-even point for sales is 3111 units.