A rancher wants to enclose an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the total shortest length of fence that the rancher can use? Hint: Part 1: State the total length of fencing required for the project as a function of x and y, where x represents the width and y the length of the field. F(x, y) = 2x+ 3y Part 2: State the area of the entire field as a function of x and y. A(x, y) =| Part 3: Find y as a function of x, using the given value of the area of the field. Part 4: Rewrite total length of fencing required as a function of x. Part 5: Find the derivative of total length of fencing required with respect to x. Part 6: Find x and y value that minimize the perimeter of the rectangular field and its perimeter.

A rancher wants to enclose an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the total shortest length of fence that the rancher can use? Hint: Part 1: State the total length of fencing required for the project as a function of x and y, where x represents the width and y the length of the field. F(x, y) = 2x+ 3y Part 2: State the area of the entire field as a function of x and y. A(x, y) =| Part 3: Find y as a function of x, using the given value of the area of the field. Part 4: Rewrite total length of fencing required as a function of x. Part 5: Find the derivative of total length of fencing required with respect to x. Part 6: Find x and y value that minimize the perimeter of the rectangular field and its perimeter.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.1: Quadratic Functions

Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...

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