Example 1.Suppose that to develop and produce a new product will cost $100,000 in time and equipment, plus $3.50 per unit for labor and materials. The selling price is $6 for each unit.

1. Construct Cost (C), Revenue (R), and Profit (P) functions in terms of x, the number of products sold?
2. How many units must sell to break even?
3. What is the break even point (BEP) in dollars?
4. What is the break even point (units) to make a profit of 20% of our investment?
5. What is the break even point (units) if the fixed cost is increased to $150,000?

Example 2. A law firm of Smith, Jones, and Greene provides accounting services for some of its clients. The person who handles this service and her secretary cost the firm an average of $80,000 a year in salary and benefits. Each client is charged a fixed rate of $300 a year for these services, and the firm is billed $50 per client for computer time, postage, and supplies.

1. Determine the total Cost (C), Revenue (R), and Profit (P) functions, in terms of x, the number of clients using the service?
2. How many clients do they need to break even?