(a) A farmer intends to fence off a rectangular pen for his pig using his barn as one of the sides. That is, no fence is needed on that side. If the enclosed area is to be 50 square feet, what are the dimensions (in feet) of the smallest amount of fence needed?

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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IV
calculus and algebra); justify that your answer does indeed yield the required absolute
Solve the following optimization problems analytically (that is, using
maximum/minimum.
(a) A farmer intends to fence off a rectangular pen for his pig using his barn as one of the sides.
That is, no fence is needed on that side. If the enclosed area is to be 50 square feet, what
are the dimensions (in feet) of the smallest amount of fence needed?
(b) An open box with a square base and a surface area of 2700 square inches is needed. Find the
dimensions of the box that would result in the largest volume?
Page 8 of 9
(c) Find the coordinates of the point on the line y = xv2 which is closest to the point
(9, 0).
Transcribed Image Text:IV calculus and algebra); justify that your answer does indeed yield the required absolute Solve the following optimization problems analytically (that is, using maximum/minimum. (a) A farmer intends to fence off a rectangular pen for his pig using his barn as one of the sides. That is, no fence is needed on that side. If the enclosed area is to be 50 square feet, what are the dimensions (in feet) of the smallest amount of fence needed? (b) An open box with a square base and a surface area of 2700 square inches is needed. Find the dimensions of the box that would result in the largest volume? Page 8 of 9 (c) Find the coordinates of the point on the line y = xv2 which is closest to the point (9, 0).
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