8) A decade from now, you reach your early twenties, decide you have an unignorable passion for milk, and go off into the country to start a dairy farm. The cows will be housed in a large rectangular pen divided in half into two smaller pens by a piece of fencing (to keep rival cows separated), as shown below. You have a total of 100 feet of fencing to use for the large rectangular pen and its dividing fence. Let the dimensions of each of the two smaller pens be l and w, as shown. a) Write a function A(w) that gives the total area A of the pens in terms of w. b) Without using your graphing calculator or Desmos, determine the exact dimensions l and w that maximize the total area of the pens for the cows. Show your work.
8) A decade from now, you reach your early twenties, decide you have an unignorable passion for milk, and go off into the country to start a dairy farm. The cows will be housed in a large rectangular pen divided in half into two smaller pens by a piece of fencing (to keep rival cows separated), as shown below. You have a total of 100 feet of fencing to use for the large rectangular pen and its dividing fence. Let the dimensions of each of the two smaller pens be l and w, as shown. a) Write a function A(w) that gives the total area A of the pens in terms of w. b) Without using your graphing calculator or Desmos, determine the exact dimensions l and w that maximize the total area of the pens for the cows. Show your work.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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Transcribed Image Text:8) A decade from now, you reach your early twenties, decide you have an unignorable passion for
milk, and go off into the country to start a dairy farm. The cows will be housed in a large rectangular
pen divided in half into two smaller pens by a piece of fencing (to keep rival cows separated), as
shown below. You have a total of 100 feet of fencing to use for the large rectangular pen and its
dividing fence. Let the dimensions of each of the two smaller pens be l and w, as shown.
a) Write a function A(w) that gives the total area A of the pens in terms of w.
b) Without using your graphing calculator or Desmos, determine the exact dimensions l and w
that maximize the total area of the pens for the cows. Show your work.
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