The Perfect Knot is a yoga studio. They offer weekly yoga classes, each one of which holds 30 students. They currently have 15 classes per week and serve a total of 450 students. The Perfect Knots owner has noticed an increased interest in Pilates lately and is considering adding Pilates classes to the studios weekly schedule. To add the Pilates classes, The Perfect Knot will need to add another instructor. They currently have three instructors on staff, each one of whom teaches five classes, and they pay the instructors $100 per class to teach. Adding the additional classes will also cost the studio an additional $50 per week in fixed costs.

The owner predicts that if they introduce the Pilates classes, 20% of their current customers will switch from yoga classes to Pilates classes, and another 10% of their current customers will attend both a yoga class and a Pilates class each week. (Read those percentages carefully.) She further predicts that introducing the Pilates classes will bring in an additional 45 new customers who will only attend Pilates classes. Currently, the studio charges $25 per week for yoga classes, but since Pilates will be new they intend to charge $20 per week for Pilates classes.

1. How many people will be taking Pilates each week if the owners predictions are correct? If the Pilates classes also fit 30 students per class, how many classes will the studio need to add?

2. How many people will be taking yoga each week after the studio introduces the Pilates classes? How many yoga classes will the studio need to offer now?

3. How much profit per week will the studio make on the new Pilates classes?

4. What will the studios gross profit per week on yoga classes be if the Pilates classes are introduced?

5. What will the studios gross profit per week on yoga classes be if the Pilates classes are not introduced?

6. Will introducing the Pilates classes be more profitable for The Perfect Knot?