Q39. - Algebra 1

Question

DVD A company that replicates DVDs spends \(1500 per day in building overhead plus \)0.80 per DVD in supplies and labor. If the DVDs sell for $1.59 per disk, how many DVDs must the company sell each day before it makes a profit?

Step-by-Step Solution

Answer

The company must sell 1898 DVDs each day before it makes a profit.

Step 1. State the formula.

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.

Step 2. List the given data.

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.

Step 3. Formulate the equation.

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,

 

$1.59x=0.80x+1500$

Step 4. Solve the equation.

Solving,

 

$1.59x=0.80x+1500$  (Given equation)

 

$1.59x-0.80x=0.80x+1500-0.80x$  (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)

 

$x\approx 1898.73$  (Simplify)

 

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

Step 5. Interpretate the obtained solution.

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.