A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60

Question

12 days ago

14

for each private lesson but has a variable cost for each lesson of $35 to pay the instructor.

1 answer:

zzz [4K] · Answer 1 · 2026-02-21T07:30:21+03:00

Answer:

a)C(x)=1500+35x

b)R(x)=60 x

c)P(x)=25x-1500

d)To achieve a break-even point, 60 lessons must be conducted.

e)If the studio conducts 82 lessons, it will earn 550.

Step-by-step explanation:

Monthly expenses including rent, utilities, insurance, and advertising total $1500.

The studio charges $60 per private lesson but incurs a $35 variable cost per lesson paid to the instructor.

a) To express the cost function C(x) for x private lessons in a month:

Fixed costs = $1500

Instructor's variable cost for each lesson = $35

The variable cost for x lessons = 35x

Thus, C(x)=1500+35x

b) To express the revenue function R(x) for x private lessons:

Earning from one lesson = $60

For x lessons = 60 x

Hence, R(x)=60 x

c) To formulate the profit function P(x) for x lessons:

Profit = Revenue - Cost

P(x)=R(x)-C(x)

P(x)=60x-1500-35x

P(x)=25x-1500

d) Finding the break-even number of lessons:

Setting R(x)=C(x)

60x=1500+35x

25x=1500

x=60

So, the studio must conduct 60 lessons to break even.

e) If 82 lessons are held, computing profit:

P(x)=25x-1500

P(82)=25(82)-1500

P(82)=550

Thus, the studio will net 550 for 82 lessons.