Market resear ice cream company price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. (a) If p denotes the price per cup (in pesos) and x denotes the demand for ice cream (in cups), express p as a linear function of x. (b) Determine the revenue function and its domain. (c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x +25,500. (d) Find the value(s) of x at the break-even points. (e) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.
Market resear ice cream company price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. (a) If p denotes the price per cup (in pesos) and x denotes the demand for ice cream (in cups), express p as a linear function of x. (b) Determine the revenue function and its domain. (c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x +25,500. (d) Find the value(s) of x at the break-even points. (e) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Answer c d e
Transcribed Image Text:1. Market research for a certain ice cream company indicates that if the price per cup of ice
cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00,
the demand will be 1100 cups.
(a) If p denotes the price per cup (in pesos) and x denotes the demand for ice cream (in
cups), express p as a linear function of x.
(b) Determine the revenue function and its domain.
(c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret.
Now, suppose it is known that the total cost of production of x cups of ice cream is given by
C(x) = 3x + 25,500.
(d) Find the value(s) of x at the break-even points.
(e) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice
cream. Compare this value with the exact profit from the sale of the 500th cup.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning