Question

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 Knot’s owner has noticed an increased interest in Pilates lately and is considering adding Pilates classes to the studio’s 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.

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

Answer 1

Calculation of profit per week from new Pilates Class

Revenue ( WN-1) $9450

(-) Cost (WN-2) $450

Profit per week    $9000

WN-1 Calculation Of revenue

Total no of Students = 450 students

Students to switch from yoga to pilates=  20%*450 =90 students

Revenue from these 90 students (after revenue loss) = $20*90 - $25*90

= $1800 - $2250

=($450)

Students who prefer to do both yoga and pilates = 10%*450= 45 Students

Revenue from these students = $20*45+$25*45

=$2025

Remaining Students = (450-90-45) Students=315 Students

Revenue from them = $25*315 = $7875

Revenue from Additional Customers = $20*45 = $900

Total Revenue = $900+$7875+$2025-$450

= $9450

WN-2 Calculation of Cost

Total no. of Instructor = 3

Cost Including Additional Cost = $100*3+$50*3 =$450