Linear Price Function

A music concert organizer has fixed costs of $5,000,000.00 and variable costs of $20.00 per attendee (ticket). Based on historical data, the price function of the tickets can be modeled as:

Calculate the following using both calculus and MS Excel:

1. Demand that maximizes 

   • revenue

   • profit

2. Maximum 

   • revenue

   • profit

3. Breakeven points

4. Develop MS Excel graphs

Answer

1. Demand Maximizing 

   • Revenue = 30,000 units

   • Profit = 29,000 units

2. Maximum 

   • Revenue =$9,000,000

   • Profit = $3,410,000

3. Breakeven Demand 

= between 10534 and 47466 units

4. Figure 2-15 shows the solution generated using MS Excel for a wide range of possible demand scenarios.