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The point just before making a profit is called the break even point. At such a point, the total cost is equal to the total earning.

A company that replicates DVDs spends $1500 per day in building overhead plus $0.80 per DVD in supplies and labor. DVDs sell for $1.59 per disk.

Let the number of DVDs that the company must sell each day before it makes a profit be x.

Then, cost of supplies and labor per day is $0.80x$.

The overhead cost per day is 1500.

Then, the total cost per day is $0.80x+1500$.

The total earning per day is $1.59x$.

According to assumption, total cost equals total earnings.

Then,

$1.59x=0.80x+1500$

Solving,

$1.59x=0.80x+1500$ (Given equation)

$1.59x鈭�0.80x=0.80x+1500鈭�0.80x$ (Subtract $0.80x$from both sides)

$0.79x=1500$ (Simplify)

$\frac{0.79x}{0.79}=\frac{1500}{0.79}$ (Divide both sides by 0.79)

$x鈮�1898.73$ (Simplify)

Rounding to the nearest integer less than the obtained value, $x=1898$.

It was assumed that the company must sell x DVDs each day before it makes a profit. Using this condition, it was obtained that $x=1898$.

So, the company must sell 1898 DVDs each day before it makes a profit.