In a certain firm, the total production cost function and a demand function are given by the equations TC = 0.16q³0.72q² +2.08q+1.46 and q=5 -0.5p. a. Is the demand function one-to-one? Explain your answer. If yes, find its inverse. b. Find the equation of the function expressing the profit P in terms of the quantity q. c. Is this profit function one-to-one? If yes, find its inverse. (Hint: use your graphing calculator.) d. Find q such that P = 6. (Hint: use your graphing calculator.)
In a certain firm, the total production cost function and a demand function are given by the equations TC = 0.16q³0.72q² +2.08q+1.46 and q=5 -0.5p. a. Is the demand function one-to-one? Explain your answer. If yes, find its inverse. b. Find the equation of the function expressing the profit P in terms of the quantity q. c. Is this profit function one-to-one? If yes, find its inverse. (Hint: use your graphing calculator.) d. Find q such that P = 6. (Hint: use your graphing calculator.)
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 8P
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Transcribed Image Text:6. In a certain firm, the total production cost function and a demand function are given by the equations
TC = 0.16q³ -0.72q² +2.08q+1.46 and
q=5 -0.5p.
a. Is the demand function one-to-one? Explain your answer. If yes, find its inverse.
b. Find the equation of the function expressing the profit P in terms of the quantity q.
c. Is this profit function one-to-one? If yes, find its inverse. (Hint: use your graphing calculator.)
d. Find q such that P = 6. (Hint: use your graphing calculator.)
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