A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio C ( x ) to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue R ( x ) for holding x private lessons for the month. c. Write a linear profit function representing the profit P ( x ) for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio C ( x ) to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue R ( x ) for holding x private lessons for the month. c. Write a linear profit function representing the profit P ( x ) for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
Solution Summary: The author explains the linear cost function that represents the fixed monthly cost of a dance studio, the variable cost to be paid to instructor for each lesson, and charges of each private lesson.
A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor.
a. Write a linear cost function representing the cost to the studio
C
(
x
)
to hold x private lessons for a given month.
b. Write a linear revenue function representing the revenue
R
(
x
)
for holding x private lessons for the month.
c. Write a linear profit function representing the profit
P
(
x
)
for holding x private lessons for the month.
d. Determine the number of private lessons that must be held for the studio to make a profit.
e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
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