TJ Technologies Ltd. is developing a new computer chip. Through market analysis, it is determined that the total cost of developing a chips is q³ C(q) = -5q² + 200g + 2000. (dollars) 3 The chips will be sold for $800 each. (i) Formulate the company's profit function P(q), then determine how many chips the company should sell in order to maximize this profit. (Recall: Profit is revenue minus cost.) (ii) The marginal cost function is defined to be the derivative C(q) of the total cost function. Find the production level q that minimizes the marginal cost C'(q).
TJ Technologies Ltd. is developing a new computer chip. Through market analysis, it is determined that the total cost of developing a chips is q³ C(q) = -5q² + 200g + 2000. (dollars) 3 The chips will be sold for $800 each. (i) Formulate the company's profit function P(q), then determine how many chips the company should sell in order to maximize this profit. (Recall: Profit is revenue minus cost.) (ii) The marginal cost function is defined to be the derivative C(q) of the total cost function. Find the production level q that minimizes the marginal cost C'(q).
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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Transcribed Image Text:3. TJ Technologies Ltd. is developing a new computer chip. Through market analysis, it is determined
that the total cost of developing a chips is
C(q)
=
9³
3
5g² + 200g + 2000. (dollars)
The chips will be sold for $800 each.
(i) Formulate the company's profit function P(q), then determine how many chips the company
should sell in order to maximize this profit.
(Recall: Profit is revenue minus cost.)
(ii) The marginal cost function is defined to be the derivative C(q) of the total cost function. Find
the production level q that minimizes the marginal cost C'(q).
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