The demand equation for your company's virtual reality video headsets is p = 2,000 q0.3 where q 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 $100 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)= R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ 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)= 780q−0.7 Evaluate P"(q) at your critical point. The result is , which means that the profit is at the critical point, and the critical point is a maximum.
The demand equation for your company's virtual reality video headsets is p = 2,000 q0.3 where q 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 $100 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)= R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ 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)= 780q−0.7 Evaluate P"(q) at your critical point. The result is , which means that the profit is 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...
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Question
The demand equation for your company's virtual reality video headsets is
p =
| 2,000 |
| q0.3 |
where q 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 $100 per headset.
(a) Find the weekly cost, revenue and profit as a function of the demand q for headsets.
C(q)=
C(q)=
R(q)=
P(q)=
(b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.)
q = headsets
What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.)
$
$
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)=
Evaluate P"(q) at your critical point. The result is , which means that the profit is at the critical point, and the critical point is a maximum.
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)=
780q−0.7
Evaluate P"(q) at your critical point. The result is , which means that the profit is at the critical point, and the critical point is a maximum.
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