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. lop rk. 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. Show work. d. Determine the number of private lessons that must be held for the studio to break-even. Show work.

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. lop rk. 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. Show work. d. Determine the number of private lessons that must be held for the studio to break-even. Show work.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

Question

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.
lop
rk.
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. Show work.
d. Determine the number of private lessons that must be held for the studio to break-even.
Show work.

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