Minimum perimeter rectangles Of all rectangles with a fixed area A, which one has the minimum perimeter? (Give the dimensions in terms of ?A.?)
Solution Step 1: Solution Step 1: Consider a rectangle of width x and length y here area of rectangle(length *width) is a constraints denote it by A Thus the constraints A=xy And perimeter of a rectangle is the objective function that is P=2(x+y) Our goal is to find the dimension of a rectangle in terms of A which gives minimum perimeter Step 2: The first step is to use the constraints to express the objective function P=2(x+y) in terms of a single variable For this A=xy A y = x Step 3: Substitute for y the objective function p becomes p=2(x+y) A =2(x+ )x P=2x+ 2A x Which is the function of single variable with x
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: minimum, rectangles, perimeter, area, give. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 6E from 4.4 chapter was answered, more than 290 students have viewed the full step-by-step answer. The answer to “Minimum perimeter rectangles Of all rectangles with a fixed area A, which one has the minimum perimeter? (Give the dimensions in terms of ?A.?)” is broken down into a number of easy to follow steps, and 24 words. The full step-by-step solution to problem: 6E from chapter: 4.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.