## A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides is to be made of material that costs 3

Question

A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 14 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.

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2 weeks 2021-11-23T14:10:44+00:00 1 Answer 0

Length of the rectangle = 9.58 feet and width = 27.14 foot

Step-by-step explanation:

Let the length of the rectangular area is = x feet

and the width of the area = y feet

Area of the rectangle = xy square feet

Or xy = 260

y = ——-(1)

Cost to fence the three sides = $3 per foot Therefore cost to fence one length and two width of the rectangular area = 3(x + 2y) Similarly cost to fence the fourth side =$14 per foot

So, the cost of the remaining length = 14x

Total cost to fence = 3(x + 2y) + 14x

Cost (C) = 3(x + 2y) + 14x

C = 3x + 6y + 14x

= 17x + 6y

From equation (1)

C =

Now we take the derivative,

C’ = 17 –

To minimize the cost of fencing,

C’ = 0

17 – = 0

= 17

x = 9.58 foot

and y =

y = 27.14 foot