A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides is to be made of material that costs 6 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.

Step-by-step explanation:

GIVEN: A fence is to be built to enclose a rectangular area of square feet. The fence along three sides is to be made of material that costs dollars per foot, and the material for the fourth side costs dollars per foot.

TO FIND: Find the dimensions of the enclosure that is most economical to construct.

SOLUTION:

Area of rectangular fence

let the length of fence

let the width of fence

let be the smaller side

Area of rectangular fence enclosure

cost of fence along three sides

cost of fence along fourth side

length of fence

cost of fence building

putting value of

to find minimum value differentiating the equation

Hence the dimensions of the enclosure that is most economical to construct are and

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step-by-step explanation: