6. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizing function, determine the domain of the optimizing function, check the second derivative for optimum value, and write the answer in complete sentence including appropriate units a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with largest possible volume. Determine the maximum volume. b) A printed page is to have 1 in. margin on all sides. The page should contain 80 sq inches of type. What dimensions of the page will minimize the area of the page while still meeting the other requirements? c) A running circuit is to be constructed in the shape of a rectangle with two semjcircles attached at the east and west ends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuit to be 2,000m (2Km), what will be the dimensions (r and I) that make the picnic area maximum? Give you answer in meters.

6. Solve the following optimization problems. Be sure to identify the constraint equation and the maximizing/minimizing function, determine the domain of the optimizing function, check the second derivative for optimum value, and write the answer in complete sentence including appropriate units a) If 1200cm² of metal is available to make a box with square base and open top, find the dimensions of the box with largest possible volume. Determine the maximum volume. b) A printed page is to have 1 in. margin on all sides. The page should contain 80 sq inches of type. What dimensions of the page will minimize the area of the page while still meeting the other requirements? c) A running circuit is to be constructed in the shape of a rectangle with two semjcircles attached at the east and west ends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuit to be 2,000m (2Km), what will be the dimensions (r and I) that make the picnic area maximum? Give you answer in meters.

Name: 6. Solve the following optimization problems. Be sure to identify the
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Description: 6. Solve the following optimization problems. Be sure to identify the constraint equation and themaximizing/minimizing function, determine the domain of the optimizing function, check the second derivative foroptimum value, and write the answer in c

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

6. Solve the following optimization problems. Be sure to identify the constraint equation and the
maximizing/minimizing function, determine the domain of the optimizing function, check the second derivative for
optimum value, and write the answer in complete sentence including appropriate units
a) If 1200cm? of metal is available to make a box with square base and open top, find the dimensions of the box
with largest possible volume. Determine the maximum volume.
b) A printed page is to have 1 in. margin on all sides. The page should contain 80 sq inches of type. What dimensions
of the page will minimize the area of the page while still meeting the other requirements?
c) A running circuit is to be constructed in the shape of a rectangle with two semicircles attached at the east and west
ends of the path (see figure). A picnic area will be set in the center of the circuit. If we want the total length of the circuit
to be 2,000m (2Km), what will be the dimensions (r and I) that make the picnic area maximum? Give you answer in
meters.

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