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

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

answer: 0.1,0.85

step-by-step explanation: