amount of material possible. (Hint: The surface area of a cylinder is S = 2πr2 + h(2πr), and its volume is V = πr2h.) (a) Draw a diagram representing this situation. (b) Write the objective and constraint functions. Objective: Constraint: (c) Use the constraint function to write the objective as a function of one variable. (d) Determine the radius and height for the absolute minimum surface area
amount of material possible. (Hint: The surface area of a cylinder is S = 2πr2 + h(2πr), and its volume is V = πr2h.) (a) Draw a diagram representing this situation. (b) Write the objective and constraint functions. Objective: Constraint: (c) Use the constraint function to write the objective as a function of one variable. (d) Determine the radius and height for the absolute minimum surface area
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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Question
You are designing a cylindrical barrel that can hold 16π m3 of crude oil. Find the radius r and height
h of the barrel that uses the least amount of material possible.
(Hint: The surface area of a cylinder is S = 2πr2 + h(2πr), and its volume is V = πr2h.)
(a) Draw a diagram representing this situation.
(b) Write the objective and constraint functions.
Objective:
Constraint:
(c) Use the constraint function to write the objective as a function of one variable.
(d) Determine the radius and height for the absolute minimum surface area
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