The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)= 110g R(q)= 1500g0.7 P(g)= 1500 g0. – 1109 (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ E Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(q)= 86977 Evaluate P"(q) at your critical point. The result is negative , which means that the profit is concave down v at the critical point, and the critical point is a maximum.
The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)= 110g R(q)= 1500g0.7 P(g)= 1500 g0. – 1109 (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ E Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(q)= 86977 Evaluate P"(q) at your critical point. The result is negative , which means that the profit is concave down v at the critical point, and the critical point is a maximum.
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
Transcribed Image Text:The demand equation for your company's virtual reality video headsets is
1,500
p =
g0.3
where g is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts
to $110 per headset.
(a) Find the weekly cost, revenue and profit as a function of the demand q for headsets.
C(q)= 110g
R(q)= 1500g0.7
P(g)= 1500 g0. – 1109
(b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.)
q = 1845
V headsets
What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.)
$ E
Second derivative test:
Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function.
P"(q)= 86977
Evaluate P"(qg) at your critical point. The result is negative
, which means that the profit is concave down v
at the critical point, and
the critical point is a maximum.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Knowledge Booster
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
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