An HVAC business owner estimates that if she sends out her winter gold star service advertisement flyer in mid October before her competition, she will book a total of 1000 appointments, at $300 each. Although, she thinks that by timing her flyer release closer to cooler weather, she will increase her appointments by 120 each week she delays the release. However, the price will likely need to drop at a rate of $15 per appointment per week due to increased competition as the weather turns colder. In addition, she estimates that she will lose approximately 20 appointments per week she delays due to cancelations. Her timeframe for releasing the flyer over the next six weeks. 1. Write an equation to determine what week out of the six week period she should release her flyer for the largest total cash return? (Hint: Releasing the flyer with no delay would be considered "Week 0" with a $300,000 return)
2. How much will she receive for her service appointments at that time?