BruceCo is planning on selling backpacks for $100 each. The company can buy the backpacks for $30.00 and have them customized for $20.00 apiece. There is a one-time set up charge of $1,000 for customization. In order for the project to go forward, the company needs to show a $10,000 profit. How many backpacks will BruceCo have to sell in order for this project to be acceptable?

Answer: BruceCo would have to sell 220 backpacks

Explanation: The projection of a $10,000 profit can be calculated properly by the equation;

Revenue - Cost = Profit

There is a one-time set up charge of 1000 and this is a fixed cost (as it does not change regardless of how many units they eventually sell). Also they would be spending $30 to buy each unit and still spend $20 to customize each. So each unit would cost $50 to acquire. If they plan on selling each unit at the rate of $100, then the total revenue would be 100 times X (where X is the number of units sold). Therefore the profit can be better projected by the equation;

Revenue - Cost = Profit

100X - (50X + 1000) = 10000

100X - 50X - 1000 = 10000

50X = 10000 + 1000

50X = 11000

Divide both sides of the equation by 50

X = 220

Therefore, BruceCo must sell 220 units (at least) in order to meet a $10,000 profit projection