Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function a=27x-x^2, where x=width, gives you the area of the dog pen in square feet. What width gives you the maximum area? Round to the nearest tenth as necessary.

Question

Mathematics

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1 October, 12:52

Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function a=27x-x^2, where x=width, gives you the area of the dog pen in square feet. What width gives you the maximum area? Round to the nearest tenth as necessary.

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Answers (1)

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Leila Casey · Answer 1

For maximum area, we take first derivative and then equalize it to zero

A (x) = 27x - x^2

A' (x) = 27 - 2x

Set that equal to zero and solve for x:

27 - 2x = 0

27 = 2x ... [ added 2x to both sides ]

13.5 = x ... [ divided both sides by 2 ]

So the area will be

A = 27 (13.5) - (13.5) ^2

= 364.5 - 182.25

= 182.3 ft^2