Problem: Richard Winchester, owner of Winchester Products, is considering introducing a new product which will require $25,000 of initial investment for plant and equipment. Winchester estimates the variable costs approximately at $10 per unit.
Q1. If the unit selling price is set at $30, how many units must be produced and sold per year in order to break even? Solve both graphically and algebraically.
Q2. Richard is not confident that demand for his product will exceed the breakeven point computed in part a. If he chooses a less appealing site and does more of the work by hand, his initial investment can be reduced to $10,000 but his unit variable cost will rise to $14.
Compare this process to the one proposed above and determine the volume of demand that should make Richard to choose this process. Show your solution both graphically and algebraically.