The cost to produce one compact disc is $1.50 plus a one-time fixed cost of $2700. The revenue received from selling one compact disc is $10
How many compact discs need to be sold to yield a positive profit?
To find the number of compact discs that need to be sold to yield a positive profit, we need to calculate the profit per unit and then divide the fixed cost by the profit per unit.
Profit per unit = Revenue per unit - Cost per unit = $10 - $1.50 = $8.50
Number of units needed to yield a positive profit = Fixed cost / Profit per unit = $2700 / $8.50 ≈ 317.65
Rounding up to the nearest whole number, we need to sell at least 318 compact discs to yield a positive profit.
To find the number of compact discs that need to be sold to yield a positive profit, we need to consider the cost and revenue associated with each disc.
The total cost to produce one compact disc is the sum of the variable cost and the fixed cost. In this case, the variable cost is $1.50. So, the total cost is $1.50 + $2700 = $2701.50.
The revenue received from selling one compact disc is $10.
To calculate the profit per disc, we subtract the total cost from the revenue per disc: Profit per disc = Revenue per disc - Total cost per disc = $10 - $2701.50.
If the profit per disc is positive, it means the revenue generated is greater than the total cost incurred, resulting in a profit.
So, we need to solve the inequality:
Profit per disc > 0
Simplifying the inequality:
$10 - $2701.50 > 0
$-2691.50 > 0
Since $-2691.50 is less than zero, it means that even selling one compact disc will not yield a positive profit.
Therefore, you cannot sell any number of compact discs to yield a positive profit in this scenario.
To determine the number of compact discs that need to be sold to yield a positive profit, we need to consider the cost and revenue per unit.
Let's calculate the profit per unit first:
Profit per unit = Revenue per unit - Cost per unit
Profit per unit = $10 - ($1.50 + $0)
Since the fixed cost of $2700 is a one-time cost and does not affect the profit per unit, we can ignore it for this calculation.
Profit per unit = $8.50
To achieve a positive profit, the profit per unit needs to be greater than zero. Therefore, we can set up the following inequality:
Profit per unit > 0
$8.50 > 0
Dividing both sides of the inequality by $8.50, we get:
1 > 0
Since 1 is greater than 0, this inequality is true.
Therefore, to yield a positive profit, at least one compact disc needs to be sold.