A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. if the area of the garden is 22 square feet, find the dimensions of the garden that minimize the cost.

Question

Mango

Mathematics

4 November, 10:25

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. if the area of the garden is 22 square feet, find the dimensions of the garden that minimize the cost.

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Titan · Answer 1

To minimize the cost, you would want the side with the brick wall to be as small as possible. as you provided no restraints to the size, a garden which is 1 foot wide by 22 feet long would be most cost effective, with 22 feet times 2 sides equaling 44 feet in total, plus one foot for the back wall. With a total of 45 feet of fence costing $450, and 1 foot of brick which will cost $20, the total cost would be $470.