Question

[Q6] [10 points] You wish to enclose a rectangular garden with a brick wall on one side, costing $30/m, and wooden fencing on the other three sides, costing $10/m. If the total area of the garden is 100m², what are the dimensions which minimize the cost?

Name: [Q6] [10 points] You wish to enclose a rectangular garden with a brick wall on one side, costing 30/m, and wooden fencing on the other three sides, costing10/m. If the total area of the garden is 100m², what are the dimensions which minimize the cost?
Uploaded: 2023-08-27T23:08:39-08:00
Duration: 1 min 18 s
Channel: Andrew Noble
Description: [Q6] [10 points] You wish to enclose a rectangular garden with a brick wall on one side, costing 30/m, and wooden fencing on the other three sides, costing10/m. If the total area of the garden is 100m², what are the dimensions which minimize the cost?

          [Q6] [10 points] You wish to enclose a rectangular garden with a brick wall on one side, costing $30/m, and wooden fencing on the other three sides, costing $10/m. If the total area of the garden is 100m², what are the dimensions which minimize the cost?

[Q6] [10 points] You wish to enclose a rectangular garden with a brick wall on one side, costing 30/m, and wooden fencing on the other three sides, costing10/m. If the total area of the garden is 100m², what are the dimensions which minimize the cost?

Added by Jeffrey M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

08/27/2023

Step 1

The area of the garden is given by A = L * W, and we know that A = 100 m^2. We need to minimize the cost function, which consists of the cost of the brick wall and the wooden fencing. The cost function is: Cost = 30L + 10(W + L + W) = 30L + 10(2W + L) = 30L + 20W Show more…

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Thanks for your feedback!

[Q6] [10 points] You wish to enclose a rectangular garden with a brick wall on one side, costing $(30)/(m), and wooden fencing on the other three sides, costing $(10)/(m). If the total area of the garden is 100m^(2), what are the dimensions which minimize the cost? This is hard please help are the dimensions which minimize the cost?