The cost to produce one compact disc is $1.75 plus a one-time fixed cost of $2500. The revenue received from selling one compact disc is $10.
how many compact discs need to be sold to yield a positive profit
Let's represent the number of compact discs sold as x.
The cost to produce x compact discs is given by the equation: cost = $1.75x + $2500.
The revenue received from selling x compact discs is given by the equation: revenue = $10x.
To find the number of compact discs needed to yield a positive profit, we need to find the value of x where revenue is greater than or equal to cost (revenue ≥ cost).
Therefore, we have the inequality:
$10x ≥ $1.75x + $2500.
To solve this inequality, we can subtract $1.75x from both sides:
$10x - $1.75x ≥ $2500.
Simplifying this, we get:
$8.25x ≥ $2500.
Next, we divide both sides by $8.25 to solve for x:
x ≥ $2500 / $8.25.
Using a calculator, we find:
x ≥ 303.03.
Since we can't sell a fraction of a CD, we round up to the nearest whole number:
x ≥ 304.
Therefore, at least 304 compact discs need to be sold to yield a positive profit.