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A paint store sells two brands of latex paint. An analysis of total sales figures indicates that the demand D (gallons/month) is modeled by D(x,y) = 210–12x² +18y, where x, y are the prices of the first and second brands, respectively. A separate study indicates that t months from now, the first brand will cost x=4+0.18t dollars/gallon and the second brand will cost y = 5 + 0.3/t dollars/gallon. At what rate the demand D will be changing in 9 months from now. Justify your answer.

A paint store sells two brands of latex paint. An analysis of total sales figures indicates that the demand D (gallons/month) is modeled by D(x,y) = 210–12x² +18y, where x, y are the prices of the first and second brands, respectively. A separate study indicates that t months from now, the first brand will cost x=4+0.18t dollars/gallon and the second brand will cost y = 5 + 0.3/t dollars/gallon. At what rate the demand D will be changing in 9 months from now. Justify your answer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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(b) A paint store sells two brands of latex paint. An analysis of total sales figures indicates that the demand D (gallons/month) is modeled by D(x, y)= 210-12x² +18y, where x, y are the prices of the first and second brands, respectively. A separate study indicates that t months from now, the first brand will cost x=4+0.18t dollars/gallon and the second brand will cost y= 5+0.3t dollars/gallon. At what rate the demand D will be changing in 9 months from now. Justify your answer.
Transcribed Image Text:(b) A paint store sells two brands of latex paint. An analysis of total sales figures indicates that the demand D (gallons/month) is modeled by D(x, y)= 210-12x² +18y, where x, y are the prices of the first and second brands, respectively. A separate study indicates that t months from now, the first brand will cost x=4+0.18t dollars/gallon and the second brand will cost y= 5+0.3t dollars/gallon. At what rate the demand D will be changing in 9 months from now. Justify your answer.
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