Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p= 200 - 0.75x. It also determines that the total cost of producing x suits is given by C(x) = 4000 + 0.5x. a) Find the total revenue, R(x). b) Find the total profit, P(x). c) How many suits must the company produce and sell in order maximize profit?

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...
icon
Related questions
Topic Video
Question
- 0.5x?.
Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p = 200 - 0.75x. It also determines that the total cost of producing x suits is given by C(x) = 4000 +
a) Find the total revenue, R(x).
b) Find the total profit, P(x).
c) How many suits must the company produce and sell in order to maximize profit?
d) What is the maximum profit?
e) What price per suit must be charged in order to maximize profit?
%D
a) R(x) =
b) P(x) =
%3D
с)
suits
d) The maximum profit is $
e) The price per unit must be $
Transcribed Image Text:- 0.5x?. Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p = 200 - 0.75x. It also determines that the total cost of producing x suits is given by C(x) = 4000 + a) Find the total revenue, R(x). b) Find the total profit, P(x). c) How many suits must the company produce and sell in order to maximize profit? d) What is the maximum profit? e) What price per suit must be charged in order to maximize profit? %D a) R(x) = b) P(x) = %3D с) suits d) The maximum profit is $ e) The price per unit must be $
5x + 500
A garden shop determines the demand function q = D(x) = 20N 4 7 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant.
%3D
(a) Find the elasticity.
(b) Find the elasticity when x = 2.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?
(a) The elasticity is
(b) When x = 2, the elasticity is
(Simplify your answer. Type an integer or a fraction)
(c) Fill in the blank below.
At $2 per plant, a small increase in price will cause the total revenue to
Transcribed Image Text:5x + 500 A garden shop determines the demand function q = D(x) = 20N 4 7 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant. %3D (a) Find the elasticity. (b) Find the elasticity when x = 2. (c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease? (a) The elasticity is (b) When x = 2, the elasticity is (Simplify your answer. Type an integer or a fraction) (c) Fill in the blank below. At $2 per plant, a small increase in price will cause the total revenue to
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 6 images

Blurred answer
Knowledge Booster
Optimization
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning