Problem
A startup called PacSafe has devised a way to make backpacks that are theft-proof targeting travelers and commuters in urban centers (once covid subsides).
Based on market research, they have realized that they can price each backpack at $60. To get the operation going, they will have to spend $50,000 lumpsum to make an e-commerce website and file for patents and trademarks.
On the manufacturing side, they have been given the following quotes from a contract manufacturer:
The contract manufacturer will charge $30 per unit if the contract is for 1500 units or less
They will charge $27 per unit if the contract is for over 1500 units but less than 3000 units
They will charge $22 per unit if the contract is for over 3000 units
How many units (backpacks) does PacSafe need to sell to break even? Please show some brief reasoning behind your answers and not just the final number.