Chapter 1, Problem 65RE

A dance studio has fixed monthly costs of $\text{\$1500}$ that include rent, utilities, insurance, and advertising. The studio charges $\text{\$60}$ for each private lesson, but has a variable cost for each lesson of $\text{\$35}$ to pay the instructor.

a. Write a linear cost function representing the cost to the studio $C\left(x\right)$ to hold $x$ private lessons for a given month.

b. Write a linear revenue function representing the revenue $R\left(x\right)$ for holding $x$ private lessons for the month.

c. Write a linear profit function representing the profit $P\left(x\right)$ 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?