Afence is to be built to enclose a rectangular area of 210 square feet. the fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 12 dollars per foot. find the dimensions of the enclosure that is most economical to construct.

Length of enclosure =18.89 foot

Width of enclosure=11.12 foot

Step-by-step explanation:

We are given that a fence is to be built to enclose a rectangular area 210 square feet.

Fence along three sides is to be made of material that costs 5 dollars per foot

and the material for the fourth side costs 12 dollars per foot.

We have to find the dimension of the enclosure that is most economical

Let x be the length and y be the width  of enclosure

We know that area of rectangle=

Cost of four sides =

Total cost=

C=

C=

Differentiate w.r.t x

Substitute

x=18.89

Differentiate w.r.t x

Substitute x=18.89

Then we get

Hence, the cost is minimum.

Length of enclosure =18.89 foot

Width of enclosure=

Hence, the dimension of the enclosure that is most economical to construct

Length=18.89 foot and width=11.12 foot

207/8 is the right