In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plans 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) = 0.022g? + 29.9q + 375 where q is the annual quanity of bales (in thousands) produced by the plant. Revenue was estimated at $67 per bale of cotton. Find the following (but be cautious and play close attention to the units): A) The Marginal Cost function: MC(q) = B) The Marginal Revenue function: MR(g) = C) The Marginal Profit function: MP(q) :
In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plans 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) = 0.022g? + 29.9q + 375 where q is the annual quanity of bales (in thousands) produced by the plant. Revenue was estimated at $67 per bale of cotton. Find the following (but be cautious and play close attention to the units): A) The Marginal Cost function: MC(q) = B) The Marginal Revenue function: MR(g) = C) The Marginal Profit function: MP(q) :
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Transcribed Image Text:In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plans 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) = 0.022q? + 29.9q + 375
where q is the annual quanity of bales (in thousands) produced by the plant. Revenue was estimated at $67
per bale of cotton.
Find the following (but be cautious and play close attention to the units):
A) The Marginal Cost function:
MC(g)
B) The Marginal Revenue function:
MR(q) =
C) The Marginal Profit function:
MP(q) =
D) The Marginal Profits for q
421 thousand bales:
MP(421) =
(Round to the nearest penny if necessary; see Part E for units.)
E) Which of the following represent the proper measurement units for the answer to Part D?
O units per dollar
dollars
thousands of dollars per unit
units
O thousands of units per dollar
dollars per unit
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