Afence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs $3 per foot. the material for the fourth side costs $9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.

The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.

Step-by-step explanation:

Given:

Area enclosed by rectangular fence is, .

Cost of fencing three sides is, c = $3 per foot.

Cost of fencing fourth side is, c' = $9 per foot.

Let a and b be the length and width of rectangle respectively.

If length of three sides be a, b, a. Then length of fourth side is b.

Then cost is,

 ...............................................................(1)

Area is,

Substitute in equation (1) as,

For minimum cost (C), the value of C' = 0. Then,

And,

Thus, the dimensions of the rectangle are 50 feet and 25 feet.

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