Question

2. There are $840 available to fence in a rectangular garden. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Consider the problem of finding the dimensions of the largest possible garden. a. Draw and label a diagram that represents this problem. b. Use calculus to find the dimensions that maximize the area of the garden. Be sure to verify that you have found a maximum value, and not a minimum. What is the maximum area that can be enclosed?

          2. There are $840 available to fence in a rectangular garden. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Consider the problem of finding the dimensions of the largest possible garden.
a. Draw and label a diagram that represents this problem.
b. Use calculus to find the dimensions that maximize the area of the garden. Be sure to verify that you have found a maximum value, and not a minimum. What is the maximum area that can be enclosed?

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2. There are 840 available to fence in a rectangular garden. The fence along three sides is to be made of material that costs6 per foot. The material for the fourth side costs 18 per foot. Consider the problem of finding the dimensions of the largest possible garden.
a. Draw and label a diagram that represents this problem.
b. Use calculus to find the dimensions that maximize the area of the garden. Be sure to verify that you have found a maximum value, and not a minimum. What is the maximum area that can be enclosed?

Added by Heather R.

Precalculus with Limits

Ron Larson 2nd Edition

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Solved by Expert Gregory Higby

08/21/2023

Step 1

Draw and label a diagram: Let the length of the garden be x and the width be y. The three sides that will be fenced with material U will have a total length of 2x + y, and the fourth side will have a length of y. The total length of fencing needed is S840, so we Show more…

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There are $840 available to fence in a rectangular garden. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per foot. Consider the problem of finding the dimensions of the largest possible garden. Draw and label a diagram that represents this problem. Use calculus to find the dimensions that maximize the area of the garden. Be sure to verify that you have found a maximum value, and not a minimum. What is the maximum area that can be enclosed?

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