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In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plants of various sizes. A quadratic model of cost (in thousands of dollars) for the largest plants was found to be very similar to: C(q) = 0.02q² +24.4g +352 where q is the annual quantity of bales (in thousands) produced by the plant. Revenue was estimated at $ 63 per bale of cotton. Find the following (but be cautious and play close attention to the units):

In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plants of various sizes. A quadratic model of cost (in thousands of dollars) for the largest plants was found to be very similar to: C(q) = 0.02q² +24.4g +352 where q is the annual quantity of bales (in thousands) produced by the plant. Revenue was estimated at $ 63 per bale of cotton. Find the following (but be cautious and play close attention to the units):

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plants of various sizes. A quadratic model of cost (in thousands of dollars) for the largest plants was found to be very similar to: C(q) = 0.02q² +24.4g +352 where q is the annual quantity of bales (in thousands) produced by the plant. Revenue was estimated at $ 63 per bale of cotton. Find the following (but be cautious and play close attention to the units): A) The Marginal Cost function: C'(q) = B) The Marginal Revenue function: R'(q) = C) The Marginal Profit function: P'(q) D) The Marginal Profits for q = 482 thousand units: P'(482) = (see Part E for units) Which of the following represent the proper units for the answer to Part D? O thousands of dollars per unit O units dollars O thousands of units per dollar O units per dollar
Transcribed Image Text:In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plants of various sizes. A quadratic model of cost (in thousands of dollars) for the largest plants was found to be very similar to: C(q) = 0.02q² +24.4g +352 where q is the annual quantity of bales (in thousands) produced by the plant. Revenue was estimated at $ 63 per bale of cotton. Find the following (but be cautious and play close attention to the units): A) The Marginal Cost function: C'(q) = B) The Marginal Revenue function: R'(q) = C) The Marginal Profit function: P'(q) D) The Marginal Profits for q = 482 thousand units: P'(482) = (see Part E for units) Which of the following represent the proper units for the answer to Part D? O thousands of dollars per unit O units dollars O thousands of units per dollar O units per dollar
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