Problem 12: a) You may have seen little conical paper cups near, say, water coolers: they are paper cups, in the shape of a (right, circular) cone, with no base (so you can put fluid in the cup). What should the height be, in terms of the radius, so as to maximize the volume with respect to the amount of used? (In other words, what dimensions maximize volume while fixing area? Or, what раper dimensions minimize area while fixing volume?) b) A steel plant has the capacity to produce x tons per day of low-grade steel and y tons per day of high-grade steel where 40-5x У- 10-х Given that the market price of low-grade steel is half that of high-grade steel, how much low-grade steel should be produced per day for maximum revenue?
Problem 12: a) You may have seen little conical paper cups near, say, water coolers: they are paper cups, in the shape of a (right, circular) cone, with no base (so you can put fluid in the cup). What should the height be, in terms of the radius, so as to maximize the volume with respect to the amount of used? (In other words, what dimensions maximize volume while fixing area? Or, what раper dimensions minimize area while fixing volume?) b) A steel plant has the capacity to produce x tons per day of low-grade steel and y tons per day of high-grade steel where 40-5x У- 10-х Given that the market price of low-grade steel is half that of high-grade steel, how much low-grade steel should be produced per day for maximum revenue?
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:Problem 12:
a) You may have seen little conical paper cups near, say, water coolers: they are paper cups, in the
shape of a (right, circular) cone, with no base (so you can put fluid in the cup). What should the
height be, in terms of the radius, so as to maximize the volume with respect to the amount of
used? (In other words, what dimensions maximize volume while fixing area? Or, what
раper
dimensions minimize area while fixing volume?)
b) A steel plant has the capacity to produce x tons per day of low-grade steel and y tons per day of
high-grade steel where
40-5x
У-
10-х
Given that the market price of low-grade steel is half that of high-grade steel, how much
low-grade steel should be produced per day for maximum revenue?
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